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Relevant bibliographies by topics / Image de Galois

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Journal articles

Academic literature on the topic 'Image de Galois'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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Journal articles on the topic "Image de Galois"

1

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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2

Greenberg, Ralph. "Galois representations with open image." Annales mathématiques du Québec 40, no. 1 (2016): 83–119. http://dx.doi.org/10.1007/s40316-015-0050-6.

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3

Boston, Nigel, and Rafe Jones. "The Image of an Arboreal Galois Representation." Pure and Applied Mathematics Quarterly 5, no. 1 (2009): 213–25. http://dx.doi.org/10.4310/pamq.2009.v5.n1.a6.

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4

Gekeler, Ernst-Ulrich. "The Galois image of twisted Carlitz modules." Journal of Number Theory 163 (June 2016): 316–30. http://dx.doi.org/10.1016/j.jnt.2015.11.021.

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5

Moon, Hyunsuk, and Yuichiro Taguchi. "Mod $p$ Galois representations of solvable image." Proceedings of the American Mathematical Society 129, no. 9 (2001): 2529–34. http://dx.doi.org/10.1090/s0002-9939-01-05894-4.

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6

Ramakrishna, Ravi. "Constructing Galois Representations with Very Large Image." Canadian Journal of Mathematics 60, no. 1 (2008): 208–21. http://dx.doi.org/10.4153/cjm-2008-009-7.

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AbstractStarting with a 2-dimensional mod p Galois representation, we construct a deformation to a power series ring in infinitely many variables over the p-adics. The image of this representation is full in the sense that it contains SL2 of this power series ring. Furthermore, all Zp specializations of this deformation are potentially semistable at p.

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7

Sharma, Devika. "Locally indecomposable Galois representations with full residual image." International Journal of Number Theory 13, no. 05 (2017): 1191–211. http://dx.doi.org/10.1142/s1793042117500646.

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We consider certain [Formula: see text]-ordinary non-CM Hida families with full residual Galois representation and give mild conditions under which every arithmetic point in these families is locally indecomposable when [Formula: see text]. The proof uses methods from deformation theory and mostly works for any odd prime [Formula: see text], but ultimately relies on the existence of a weight [Formula: see text] form in an auxiliary family which is available only for [Formula: see text]. We end by giving several non-trivial examples of [Formula: see text]-ordinary non-CM locally indecomposable modular forms of small level with full residual Galois representation.

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8

Boston, Nigel, and David T. Ose. "Characteristic p Galois Representations That Arise from Drinfeld Modules." Canadian Mathematical Bulletin 43, no. 3 (2000): 282–93. http://dx.doi.org/10.4153/cmb-2000-035-5.

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AbstractWe examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group’s action on the division points of an appropriate Drinfeld module.

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9

Koch, Alan. "Abelian maps, bi-skew braces, and opposite pairs of Hopf-Galois structures." Proceedings of the American Mathematical Society, Series B 8, no. 16 (2021): 189–203. http://dx.doi.org/10.1090/bproc/87.

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Let G G be a finite nonabelian group, and let ψ : G → G \psi :G\to G be a homomorphism with abelian image. We show how ψ \psi gives rise to two Hopf-Galois structures on a Galois extension L / K L/K with Galois group (isomorphic to) G G ; one of these structures generalizes the construction given by a “fixed point free abelian endomorphism” introduced by Childs in 2013. We construct the skew left brace corresponding to each of the two Hopf-Galois structures above. We will show that one of the skew left braces is in fact a bi-skew brace, allowing us to obtain four set-theoretic solutions to the Yang-Baxter equation as well as a pair of Hopf-Galois structures on a (potentially) different finite Galois extension.

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10

Conti, Andrea. "Galois level and congruence ideal for -adic families of finite slope Siegel modular forms." Compositio Mathematica 155, no. 4 (2019): 776–831. http://dx.doi.org/10.1112/s0010437x19007048.

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We consider families of Siegel eigenforms of genus $2$ and finite slope, defined as local pieces of an eigenvariety and equipped with a suitable integral structure. Under some assumptions on the residual image, we show that the image of the Galois representation associated with a family is big, in the sense that a Lie algebra attached to it contains a congruence subalgebra of non-zero level. We call the Galois level of the family the largest such level. We show that it is trivial when the residual representation has full image. When the residual representation is a symmetric cube, the zero locus defined by the Galois level of the family admits an automorphic description: it is the locus of points that arise from overconvergent eigenforms for $\operatorname{GL}_{2}$, via a $p$-adic Langlands lift attached to the symmetric cube representation. Our proof goes via the comparison of the Galois level with a ‘fortuitous’ congruence ideal. Some of the $p$-adic lifts are interpolated by a morphism of rigid analytic spaces from an eigencurve for $\operatorname{GL}_{2}$ to an eigenvariety for $\operatorname{GSp}_{4}$, while the remainder appear as isolated points on the eigenvariety.

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