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Journal articles on the topic 'Galois cover'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Baik, Hyungryul, Farbod Shokrieh, and Chenxi Wu. "Limits of canonical forms on towers of Riemann surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 764 (2020): 287–304. http://dx.doi.org/10.1515/crelle-2019-0007.

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AbstractWe prove a generalized version of Kazhdan’s theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence {\{S_{n}\rightarrow S\}} of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on {S_{n}}’s converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss–Bo

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Kontogeorgis, Aristides, and Panagiotis Paramantzoglou. "Galois action on homology of generalized Fermat Curves." Quarterly Journal of Mathematics 71, no. 4 (2020): 1377–417. http://dx.doi.org/10.1093/qmath/haaa038.

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Abstract The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups H. We provide a unified study of the action of both cover Galois group H and the absolute Galois group $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on the pro-$\ell$ homology of the curves in study. Also the relation to the pro-$\ell$ Burau representation is investigated.

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König, Joachim. "On the mod-p distribution of discriminants of G-extensions." International Journal of Number Theory 16, no. 04 (2019): 767–85. http://dx.doi.org/10.1142/s1793042120500396.

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This paper was motivated by a recent paper by Krumm and Pollack ([Twists of hyperelliptic curves by integers in progressions modulo [Formula: see text], preprint (2018); https://arXiv.org/abs/1807.00972] ) investigating modulo-[Formula: see text] behavior of quadratic twists with rational points of a given hyperelliptic curve, conditional on the abc-conjecture. We extend those results to twisted Galois covers with arbitrary Galois groups. The main point of this generalization is to interpret those results as statements about the sets of specializations of a given Galois cover under restriction

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Garnek, Jędrzej. "$p$-group Galois covers of curves in characteristic $p$. II." Documenta Mathematica 30, no. 2 (2025): 347–77. https://doi.org/10.4171/dm/998.

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Let k be an algebraically closed field of characteristic p>0 and let G be a finite p -group. The results of Harbater, Katz and Gabber associate to every k -linear action of G on k\llbracket t\rrbracket an HKG-cover, i.e. a G -cover of the projective line ramified only over \infty . In this paper we relate the HKG-covers to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of G . To this end, we present a new way of computing cohomologies of HKG-covers. As an application of our results, we compute the equivariant structure of the de Rham

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AMRAM, MEIRAV, MINA TEICHER та UZI VISHNE. "THE FUNDAMENTAL GROUP OF GALOIS COVER OF THE SURFACE 𝕋 × 𝕋". International Journal of Algebra and Computation 18, № 08 (2008): 1259–82. http://dx.doi.org/10.1142/s0218196708004895.

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This is the final paper in a series of four, concerning the surface 𝕋 × 𝕋 embedded in ℂℙ8, where 𝕋 is the one-dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto ℂℙ2, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

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Kedlaya, Kiran S. "On the Geometry ofp-Typical Covers in Characteristicp." Canadian Journal of Mathematics 60, no. 1 (2008): 140–63. http://dx.doi.org/10.4153/cjm-2008-006-8.

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AbstractForpa prime, ap-typical cover of a connected scheme on whichp= 0 is a finite étale cover whose monodromy group (i.e.,the Galois group of its normal closure) is ap-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors; building on work of Katz, we demonstrate some of these. These include a criterion for when a morphism induces an isomorphism of thep-typical quotients of the étale fundamental groups, and a decomposition theorem forp-typical covers of polynomial rings over an algebraically closed field.

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AMRAM, MEIRAV, MINA TEICHER, and UZI VISHNE. "THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)." International Journal of Algebra and Computation 17, no. 03 (2007): 507–25. http://dx.doi.org/10.1142/s0218196707003780.

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This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is [Formula: see text] where c = gcd (a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois co

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8

Shirane, Taketo. "Connected Numbers and the Embedded Topology of Plane Curves." Canadian Mathematical Bulletin 61, no. 3 (2018): 650–58. http://dx.doi.org/10.4153/cmb-2017-066-5.

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AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

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9

PARDINI, RITA, and FRANCESCA TOVENA. "ON THE FUNDAMENTAL GROUP OF AN ABELIAN COVER." International Journal of Mathematics 06, no. 05 (1995): 767–89. http://dx.doi.org/10.1142/s0129167x9500033x.

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Let X, Y be smooth complex projective varieties of dimension n≥2 and let f: Y→X be a totally ramified abelian cover. Assume that the components of the branch divisor of f are ample. Then the map f*: π1(Y)→π1(X) is surjective and gives rise to a central extension: [Formula: see text] where K is a finite group. Here we show how the kernel K and the cohomology class c(f) ∈ H2(π1(X), K) of (1) can be computed in terms of the Chern classes of the components of the branch divisor of f and of the eigensheaves of [Formula: see text] under the action of the Galois group. Using this result, for any inte

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10

Ksir, Amy E. "Dimensions of Prym varieties." International Journal of Mathematics and Mathematical Sciences 26, no. 2 (2001): 107–16. http://dx.doi.org/10.1155/s016117120101153x.

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Given a tame Galois branched cover of curvesπ:X→Ywith any finite Galois groupGwhose representations are rational, we compute the dimension of the (generalized) Prym varietyPrymρ(X)corresponding to any irreducible representationρofG. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. However, the formula is much more general and its computation and proof are entirely algebraic.

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11

Witthaus, Robin. "None." Journal de théorie des nombres de Bordeaux 37, no. 1 (2025): 189–235. https://doi.org/10.5802/jtnb.1319.

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We extend Colmez’s functor defined for GL 2 (Q p ) to the category of finitely generated smooth admissible mod-p representations of the two-fold metaplectic cover of GL 2 (Q p ) – a central extension by the roots of unity μ 2 in Q. We compute the images of the absolutely irreducible objects, which are genuine, i.e. on which the central subgroup μ 2 acts via the non-trivial character, and obtain a bijection between genuine supersingular representations and four-dimensional irreducible Galois representations invariant under twist by all characters of order two. Restricted to genuine representati

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12

Bhatt, Bhargav, Javier Carvajal-Rojas, Patrick Graf, Karl Schwede, and Kevin Tucker. "Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes." International Mathematics Research Notices 2019, no. 14 (2017): 4325–39. http://dx.doi.org/10.1093/imrn/rnx253.

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Abstract We prove that a strongly $F$-regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $\tilde X \to X$ such that the étale fundamental groups of $\tilde X$ and $\tilde X_{{\mathrm{reg}}}$ agree. Equivalently, every finite étale cover of $\tilde X_{{\mathrm{reg}}}$ extends to a finite étale cover of $\tilde X$. This is analogous to a result for complex klt varieties by Greb, Kebekus, and Peternell.

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13

OTSUKI, Hideaki, and Tomio HIRATA. "The Biclique Cover Problem and the Modified Galois Lattice." IEICE Transactions on Information and Systems E98.D, no. 3 (2015): 497–502. http://dx.doi.org/10.1587/transinf.2014fcp0019.

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14

Amram, Meirav, David Goldberg, Mina Teicher та Uzi Vishne. "The fundamental group of a Galois cover of ℂℙ1×T". Algebraic & Geometric Topology 2, № 1 (2002): 403–32. http://dx.doi.org/10.2140/agt.2002.2.403.

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15

Abughazalah, Nabilah, and Majid Khan. "An Efficient Information Hiding Mechanism Based on Confusion Component over Local Ring and Moore-Penrose Pseudo Inverse." WSEAS TRANSACTIONS ON MATHEMATICS 20 (March 2, 2021): 24–36. http://dx.doi.org/10.37394/23206.2021.20.3.

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The basic requirement by adding confusion is to ensure the confidentiality of the secret information. In the present article, we have suggested new methodology for the construction of nonlinear confusion component. This confusion component is used for enciphering the secret information and hiding it in a cover medium by proposed scheme. The proposed scheme is based on ring structure instead of Galois field mechanism. To provide multi-layer security, secret information is first encrypted by using confusion component and then utilized three different substitution boxes (S-boxes) to hide into the

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16

Hwangk, Yoon Sung, and Bill Jacob. "Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory." Canadian Journal of Mathematics 47, no. 3 (1995): 527–43. http://dx.doi.org/10.4153/cjm-1995-029-4.

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AbstractLet F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form

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17

Anderson, David E. "A cusp singularity with no Galois cover by a complete intersection." Proceedings of the American Mathematical Society 132, no. 9 (2004): 2517–27. http://dx.doi.org/10.1090/s0002-9939-04-07302-2.

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18

Corvaja, Pietro, Julian Lawrence Demeio, Ariyan Javanpeykar, Davide Lombardo, and Umberto Zannier. "On the distribution of rational points on ramified covers of abelian varieties." Compositio Mathematica 158, no. 11 (2022): 2109–55. http://dx.doi.org/10.1112/s0010437x22007746.

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We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields $k$ of characteristic zero. For example, given a ramified cover $\pi : X \to A$ , where $A$ is an abelian variety over $k$ with a dense set of $k$ -rational points, we prove that there is a finite-index coset $C \subset A(k)$ such that $\pi (X(k))$ is disjoint from $C$ . Our results do not seem to be in the range of other methods available at present; they confirm predictions coming from Lang's conjectures on rational points, and also go in the direction of an issu

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19

Ford, Timothy J. "The group of units on an affine variety." Journal of Algebra and Its Applications 13, no. 08 (2014): 1450065. http://dx.doi.org/10.1142/s0219498814500650.

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The object of study is the group of units 𝒪*(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X → 𝔸m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that 𝒪*(X) is equal to k*, the non-zero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at in

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20

Kanemitsu, Akihiro, and Kiwamu Watanabe. "Projective varieties with nef tangent bundle in positive characteristic." Compositio Mathematica 159, no. 9 (2023): 1974–99. http://dx.doi.org/10.1112/s0010437x23007376.

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Let $X$ be a smooth projective variety defined over an algebraically closed field of positive characteristic $p$ whose tangent bundle is nef. We prove that $X$ admits a smooth morphism $X \to M$ such that the fibers are Fano varieties with nef tangent bundle and $T_M$ is numerically flat. We also prove that extremal contractions exist as smooth morphisms. As an application, we prove that, if the Frobenius morphism can be lifted modulo $p^2$ , then $X$ admits, up to a finite étale Galois cover, a smooth morphism onto an ordinary abelian variety whose fibers are products of projective spaces.

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Castryck, Wouter, Floris Vermeulen, and Yongqiang Zhao. "Scrollar invariants, syzygies and representations of the symmetric group." Journal für die reine und angewandte Mathematik (Crelles Journal) 2023, no. 796 (2023): 117–59. http://dx.doi.org/10.1515/crelle-2022-0088.

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Abstract We give an explicit minimal graded free resolution, in terms of representations of the symmetric group S d {S_{d}} , of a Galois-theoretic configuration of d points in 𝐏 d - 2 {\mathbf{P}^{d-2}} that was studied by Bhargava in the context of ring parametrizations. When applied to the geometric generic fiber of a simply branched degree d cover of 𝐏 1 {\mathbf{P}^{1}} by a relatively canonically embedded curve C, our construction gives a new interpretation for the splitting types of the syzygy bundles appearing in its relative minimal resolution. Concretely, our work implies that all th

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Amram, Meirav, Mina Teicher та Uzi Vishne. "The Coxeter Quotient of the Fundamental Group of a Galois Cover of 𝕋 × 𝕋". Communications in Algebra 34, № 1 (2006): 89–106. http://dx.doi.org/10.1080/00927870500346024.

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23

Amram, Meirav, Sheng Li Tan, Wan Yuan Xu та Michael Yoshpe. "Calculating the Fundamental Group of Galois Cover of the (2,3)-embedding of ℂℙ1 × T". Acta Mathematica Sinica, English Series 36, № 3 (2020): 273–91. http://dx.doi.org/10.1007/s10114-020-9220-9.

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24

Zhenhua Tan, Danke Wu, Hong Li, Tianhan Gao, and Nan Guo. "Hierarchical Threshold Secret Image Sharing Scheme Based on Birkhoff Interpolation and Matrix Projection." Research Briefs on Information and Communication Technology Evolution 4 (October 15, 2018): 125–33. http://dx.doi.org/10.56801/rebicte.v4i.73.

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This paper focuses on how to protect confidential image based on hierarchical threshold secret sharingscheme, against fake shadow attacks, collusion attacks and shadow information leakage problem.Inspired by existing research, we propose a novel hierarchical threshold secret sharing scheme basedon Birkhoff interpolation and matrix projection, hierarchical secret distribution mathematical processesand hierarchical threshold reconstruction mathematical processes are proposed in detail inthis paper, by designing random matrix generation, polynomial multiple derivatives, and Birkhoffinterpolation

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25

Rito, Carlos. "Cuspidal quintics and surfaces with , and 5-torsion." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 42–53. http://dx.doi.org/10.1112/s1461157015000315.

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If $S$ is a quintic surface in $\mathbb{P}^{3}$ with singular set 15 3-divisible ordinary cusps, then there is a Galois triple cover ${\it\phi}:X\rightarrow S$ branched only at the cusps such that $p_{g}(X)=4$, $q(X)=0$, $K_{X}^{2}=15$ and ${\it\phi}$ is the canonical map of $X$. We use computer algebra to search for such quintics having a free action of $\mathbb{Z}_{5}$, so that $X/\mathbb{Z}_{5}$ is a smooth minimal surface of general type with $p_{g}=0$ and $K^{2}=3$. We find two different quintics, one of which is the van der Geer–Zagier quintic; the other is new.We also construct a quinti

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Siddiqui, Nasir, Fahim Yousaf, Fiza Murtaza, et al. "A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field." PLOS ONE 15, no. 11 (2020): e0241890. http://dx.doi.org/10.1371/journal.pone.0241890.

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Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cry

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27

Iovita, Adrian, Jackson S. Morrow, and Alexandru Zaharescu. "On p-adic uniformization of abelian varieties with good reduction." Compositio Mathematica 158, no. 7 (2022): 1449–76. http://dx.doi.org/10.1112/s0010437x22007643.

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Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of ${{\mathbb {Q}}}_p$ , let $K$ be the maximal unramified extension of ${{\mathbb {Q}}}_p$ , ${{\overline {K}}}$ some fixed algebraic closure of $K$ , and ${{\mathbb {C}}}_p$ be the completion of ${{\overline {K}}}$ . Let $G_F$ be the absolute Galois group of $F$ . Let $A$ be an abelian variety defined over $F$ , with good reduction. Classically, the Fontaine integral was seen as a Hodge–Tate comparison morphism, i.e. as a map $\varphi _{A} \otimes 1_{{{\mathbb {C}}}_p}\colon T_p(A)\otimes _{{{\mathbb {Z}}}_p}{{\mathbb

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BISWAS, INDRANIL. "PRINCIPAL BUNDLES ON RATIONALLY CONNECTED FIBRATIONS OVER ABELIAN VARIETIES." International Journal of Mathematics 20, no. 02 (2009): 167–88. http://dx.doi.org/10.1142/s0129167x0900525x.

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Let f : M → A be a smooth surjective algebraic morphism, where M is a connected complex projective manifold and A a complex abelian variety, such that all the fibers of f are rationally connected. We show that an algebraic principal G-bundle EG over M admits a flat holomorphic connection if EG admits a holomorphic connection; here G is any connected reductive linear algebraic group defined over ℂ. We also show that EG admits a holomorphic connection if and only if any of the following three statements holds. (1) The principal G-bundle EG is semistable, c2( ad (EG)) = 0, and all the line bundle

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29

van Bommel, Raymond. "Inverse Galois problem for ordinary curves." International Journal of Number Theory 14, no. 05 (2018): 1305–15. http://dx.doi.org/10.1142/s1793042118500811.

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We consider the inverse Galois problem over function fields of positive characteristic [Formula: see text], for example, over the projective line. We describe a method to construct certain Galois covers of the projective line and other curves, which are ordinary in the sense that their Jacobian has maximal [Formula: see text]-torsion. We do this by constructing Galois covers of ordinary semi-stable curves, and then deforming them into smooth Galois covers.

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30

TOMAŠIĆ, IVAN. "TWISTED GALOIS STRATIFICATION." Nagoya Mathematical Journal 222, no. 1 (2016): 1–60. http://dx.doi.org/10.1017/nmj.2016.9.

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We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula over fields with powers of Frobenius. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic–geometric description of definable sets over fields with Frobenii in terms of twisted Galois formulas associated with finite Galois covers of difference schemes.

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Amram, Meirav, Cheng Gong, Sheng-Li Tan, Mina Teicher, and Wan-Yuan Xu. "The fundamental groups of Galois covers of planar Zappatic deformations of type Ek." International Journal of Algebra and Computation 29, no. 06 (2019): 905–25. http://dx.doi.org/10.1142/s0218196719500358.

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In this paper, we investigate the fundamental groups of Galois covers of planar Zappatic deformations of type [Formula: see text]. Using Moishezon–Teicher’s algorithm, we prove that the Galois covers of the generic fiber of planar Zappatic deformations of type [Formula: see text] [Formula: see text] are simply-connected; we also compute their Chern numbers.

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Malle, Gunter, and David P. Roberts. "Number Fields with Discriminant ±2a3b and Galois Group An or Sn." LMS Journal of Computation and Mathematics 8 (2005): 80–101. http://dx.doi.org/10.1112/s1461157000000905.

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AbstractThe authors present three-point and four-point covers having bad reduction at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 12, 18, 28, and 33. By specializing these covers, they obtain number fields ramified at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 11, 12, 17, 18, 25, 28, 30, and 33.

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Xiao, Gang. "Galois covers between $K3$ surfaces." Annales de l’institut Fourier 46, no. 1 (1996): 73–88. http://dx.doi.org/10.5802/aif.1507.

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AMRAM, MEIRAV, RUTH LAWRENCE, and UZI VISHNE. "ARTIN COVERS OF THE BRAID GROUPS." Journal of Knot Theory and Its Ramifications 21, no. 07 (2012): 1250061. http://dx.doi.org/10.1142/s0218216512500617.

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Computation of fundamental groups of Galois covers recently led to the construction and analysis of Coxeter covers of the symmetric groups [L. H. Rowen, M. Teicher and U. Vishne, Coxeter covers of the symmetric groups, J. Group Theory8 (2005) 139–169]. In this paper we consider analog covers of Artin's braid groups, and completely describe the induced geometric extensions of the braid group.

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35

Harbater, David. "Galois Covers of an Arithmetic Surface." American Journal of Mathematics 110, no. 5 (1988): 849. http://dx.doi.org/10.2307/2374696.

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36

TONINI, FABIO. "RAMIFIED GALOIS COVERS VIA MONOIDAL FUNCTORS." Transformation Groups 22, no. 3 (2016): 845–68. http://dx.doi.org/10.1007/s00031-016-9395-4.

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Moishezon, B., A. Robb, and M. Teicher. "On Galois covers of Hirzebruch surfaces." Mathematische Annalen 305, no. 1 (1996): 493–539. http://dx.doi.org/10.1007/bf01444235.

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38

Crespo, Teresa, and Zbigniew Hajto. "Differential Galois realization of double covers." Annales de l’institut Fourier 52, no. 4 (2002): 1017–25. http://dx.doi.org/10.5802/aif.1908.

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39

Pappas, Georgios. "Galois module structure of unramified covers." Mathematische Annalen 341, no. 1 (2007): 71–97. http://dx.doi.org/10.1007/s00208-007-0183-2.

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40

Gekeler, Ernst-Ulrich. "Towers of GL($r$)-type of modular curves." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (2019): 87–141. http://dx.doi.org/10.1515/crelle-2017-0012.

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Abstract We construct Galois covers {X^{r,k}(N)} over {{\mathbb{P}}^{1}/{\mathbb{F}}_{q}(T)} with Galois groups close to {{\rm GL}(r,{\mathbb{F}}_{q}[T]/(N))} ( {r\geq 3} ) and rationality and ramification properties similar to those of classical modular curves {X(N)} over {{\mathbb{P}}^{1}/{\mathbb{Q}}} . As application we find plenty of good towers (with \limsup{\frac{\text{number~{}of~{}rational~{}points}}{{\rm genus}}>0} ) of curves over the field {{\mathbb{F}}_{q^{r}}} with {q^{r}} elements.

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41

Poonen, Bjorn. "Unramified covers of Galois covers of low genus curves." Mathematical Research Letters 12, no. 4 (2005): 475–81. http://dx.doi.org/10.4310/mrl.2005.v12.n4.a3.

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42

Amram, Meirav, та David Goldberg. "Higher degree Galois covers of ℂℙ1×T". Algebraic & Geometric Topology 4, № 2 (2004): 841–59. http://dx.doi.org/10.2140/agt.2004.4.841.

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43

Eberhart, Ryan, and Hilaf Hasson. "Arithmetic descent of specializations of Galois covers." Functiones et Approximatio Commentarii Mathematici 56, no. 2 (2017): 259–70. http://dx.doi.org/10.7169/facm/1613.

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Obus, Andrew. "Good reduction of three-point Galois covers." Algebraic Geometry 4, no. 2 (2017): 247–62. http://dx.doi.org/10.14231/ag-2017-013.

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Gallego, Francisco Javier, and Bangere P. Purnaprajna. "Classification of quadruple Galois canonical covers I." Transactions of the American Mathematical Society 360, no. 10 (2008): 5489–507. http://dx.doi.org/10.1090/s0002-9947-08-04587-x.

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Eberhart, Ryan. "Galois branched covers with fixed ramification locus." Journal of Pure and Applied Algebra 219, no. 5 (2015): 1592–603. http://dx.doi.org/10.1016/j.jpaa.2014.06.017.

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Dèbes, Pierre, and Nour Ghazi. "Galois Covers and the Hilbert-Grunwald Property." Annales de l’institut Fourier 62, no. 3 (2012): 989–1013. http://dx.doi.org/10.5802/aif.2714.

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Pop, Florian. "�tale Galois covers of affine smooth curves." Inventiones Mathematicae 120, no. 1 (1995): 555–78. http://dx.doi.org/10.1007/bf01241142.

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Gallego, Francisco Javier, and Bangere P. Purnaprajna. "Classification of quadruple Galois canonical covers, II." Journal of Algebra 312, no. 2 (2007): 798–828. http://dx.doi.org/10.1016/j.jalgebra.2006.11.011.

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TAKAHASHI, Nobuyoshi. "QUANDLES ASSOCIATED TO GALOIS COVERS OF ARITHMETIC SCHEMES." Kyushu Journal of Mathematics 73, no. 1 (2019): 145–64. http://dx.doi.org/10.2206/kyushujm.73.145.

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