Relevant bibliographies by topics / Modules de Drinfeld

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Modules de Drinfeld'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 December 2024

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Journal articles on the topic "Modules de Drinfeld"

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Shi, Gui-Qi, Xiao-Li Fang, and Blas Torrecillas. "Generalized Yetter–Drinfeld (quasi)modules and Yetter–Drinfeld–Long bi(quasi)modules for Hopf quasigroups." Journal of Algebra and Its Applications 18, no. 02 (2019): 1950034. http://dx.doi.org/10.1142/s0219498819500348.

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As generalizations of Yetter–Drinfeld module over a Hopf quasigroup, we introduce the notions of Yetter–Drinfeld–Long bimodule and generalize the Yetter–Drinfeld module over a Hopf quasigroup in this paper, and show that the category of Yetter–Drinfeld–Long bimodules [Formula: see text] over Hopf quasigroups is braided, which generalizes the results in Alonso Álvarez et al. [Projections and Yetter–Drinfeld modules over Hopf (co)quasigroups, J. Algebra 443 (2015) 153–199]. We also prove that the category of [Formula: see text] having all the categories of generalized Yetter–Drinfeld modules [Fo
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Fang, Xiao-Li, Tae-Hwa Kim, and Xiao-Hui Zhang. "Symmetry and pseudosymmetry of v-Yetter–Drinfeld categories for Hom–Hopf algebras." International Journal of Geometric Methods in Modern Physics 14, no. 09 (2017): 1750129. http://dx.doi.org/10.1142/s0219887817501298.

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The purpose of this paper is to introduce the category of [Formula: see text]-Yetter–Drinfeld modules ([Formula: see text]) over a Hom–Hopf algebra. We first prove that every category of [Formula: see text]-Yetter–Drinfeld modules over a Hom–Hopf algebra with a bijective antipode [Formula: see text] is a braided tensor category and that every [Formula: see text]-Yetter–Drinfeld module can provide the solution of the Hom–Yang–Baxter equation. Secondly, we find sufficient and necessary conditions for [Formula: see text] to be symmetric and pseudosymmetric, respectively. Finally, we construct exa
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Sánchez–Mirafuentes, Marco Antonio, Julio Cesar Salas–Torres, and Gabriel Villa–Salvador. "Cogalois theory and drinfeld modules." Journal of Algebra and Its Applications 19, no. 01 (2019): 2050001. http://dx.doi.org/10.1142/s0219498820500012.

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In this paper, we generalize the results of [M. Sánchez-Mirafuentes and G. Villa–Salvador, Radical extensions for the Carlitz module, J. Algebra 398 (2014) 284–302] to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension [Formula: see text].
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Rosen, Michael. "Formal Drinfeld modules." Journal of Number Theory 103, no. 2 (2003): 234–56. http://dx.doi.org/10.1016/s0022-314x(03)00111-2.

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Bae, Sunghan, and Pyung-Lyun Kang. "On Tate-Drinfeld Modules." Canadian Mathematical Bulletin 35, no. 2 (1992): 145–51. http://dx.doi.org/10.4153/cmb-1992-021-1.

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Guo, Yaguo, and Sinlin Yang. "Projective class rings of the category of Yetter-Drinfeld modules over the $ 2 $-rank Taft algebra." Electronic Research Archive 31, no. 8 (2023): 5006–24. http://dx.doi.org/10.3934/era.2023256.

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<abstract><p>In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over the $ 2 $-rank Taft algebra $ \mathcal{\bar{A}} $ are construted and classified by Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class ring of the category of Yetter-Drinfeld modules over $ \mathcal{\bar{A}} $ is described explicitly by generators and relations.</p></abstract>
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Guo, Yaguo, and Shilin Yang. "Projective class rings of a kind of category of Yetter-Drinfeld modules." AIMS Mathematics 8, no. 5 (2023): 10997–1014. http://dx.doi.org/10.3934/math.2023557.

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<abstract><p>In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed $ 8m $-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.</p></abstract>
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El-Guindy, Ahmad. "Legendre Drinfeld modules and universal supersingular polynomials." International Journal of Number Theory 10, no. 05 (2014): 1277–89. http://dx.doi.org/10.1142/s1793042114500262.

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We introduce a certain family of Drinfeld modules that we propose as analogues of the Legendre normal form elliptic curves. We exhibit explicit formulas for a certain period of such Drinfeld modules as well as formulas for the supersingular locus in that family, establishing a connection between these two kinds of formulas. Lastly, we also provide a closed formula for the supersingular polynomial in the j-invariant for generic Drinfeld modules.
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Yu, Jing. "Transcendence and Drinfeld modules." Inventiones Mathematicae 83, no. 3 (1986): 507–17. http://dx.doi.org/10.1007/bf01394419.

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Gekele, Ernst-Ulrich. "On finite Drinfeld modules." Journal of Algebra 141, no. 1 (1991): 187–203. http://dx.doi.org/10.1016/0021-8693(91)90211-p.

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Dissertations / Theses on the topic "Modules de Drinfeld"

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Basson, Dirk Johannes. "On the coefficients of Drinfeld modular forms of higher rank." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86387.

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Thesis (PhD)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: Rank 2 Drinfeld modular forms have been studied for more than 30 years, and while it is known that a higher rank theory could be possible, higher rank Drinfeld modular forms have only recently been de ned. In 1988 Gekeler published [Ge2] in which he studies the coe cients of rank 2 Drinfeld modular forms. The goal of this thesis is to perform a similar study of the coe cients of higher rank Drinfeld modular forms. The main results are that the coe cients themselves are (weak) Drinfeld modular forms, a product formula for
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David, Chantal. "Supersingular reduction of Drinfeld modules." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41268.

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Let $ phi$ be a rank 2 Drinfeld A-module over the ring A of polynomials over some finite field $F sb{q}$. We give a bound on the norm of those primes p of A which are factors of $P sb{d}(j sb phi)$ for two distinct polynomials d $ in$ A. We then show that the number of supersingular primes of $ phi$ with norm smaller than x is $ gg log log$ x. We investigate the endomorphism rings of supersingular Drinfeld A-modules over finite fields. Under a mild hypothesis, this leads to an upper bound of $x sp{3/4} log sp2 x$ for the number of supersingular primes of $ phi$, with even degree, and norm smal
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Dion, Sophie. "Analyse diophantienne et modules de Drinfeld." Lille 1, 2002. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/2002/50376-2002-61-62.pdf.

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Armana, Cécile. "Torsion rationnelle des modules de Drinfeld." Phd thesis, Université Paris-Diderot - Paris VII, 2008. http://tel.archives-ouvertes.fr/tel-00338117.

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Cette thèse étudie l'existence de points de torsion pour les modules de Drinfeld de rang 2 sur des extensions finies de F_q(T), pour q puissance d'un nombre premier. Notre approche suit celle de Mazur et Merel pour la torsion des courbes elliptiques sur les corps de nombres : nous introduisons un quotient de la jacobienne d'une courbe modulaire de Drinfeld, défini à l'aide d'un symbole modulaire de Teitelbaum particulier, et étudions ses propriétés. Sous une hypothèse de dualité entre algèbre de Hecke et formes modulaires pour F_q[T], ainsi qu'une hypothèse technique mineure, on montre le résu
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Armana, Cécile. "Torsion rationnelle des modules de Drinfeld." Phd thesis, Paris 7, 2008. https://theses.hal.science/tel-00338117v2.

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Cette thèse étudie l'existence de points de torsion pour les modules de Drinfeld de rang 2 sur des extensions finies de Fq(T), pour q puissance d'un nombre premier. Notre approche suit celle de Mazur et Merel pour la torsion des courbes elliptiques sur les corps de nombres : nous introduisons un quotient de la jacobienne d'une courbe modulaire de Drinfeld, défini à l'aide d'un symbole modulaire de Teitelbaum particulier, et étudions ses propriétés. Sous une hypothèse de dualité entre algèbre de Hecke et formes modulaires pour Fq[T], ainsi qu'une hypothèse technique mineure, on montre le résult
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Angles, Bruno. "Modules de Drinfeld sur les corps finis." Toulouse 3, 1994. http://www.theses.fr/1994TOU30238.

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Soit l un corps fini, nous determinons les sous-anneaux des polynomes de ore sur l qui sont anneaux d'endomorphismes de modules de drinfeld. D'autre part, si on fixe un module de drinfeld sur l, on etudie l'action du frobenius de l sur la cohomologie de de rham, sur les modules de tate et sur la cohomologie cristalline du module de drinfeld considere. On montre que dans tous les cas, le polynome caracteristique de l'action du frobenius est determine par son polynome minimal
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Leudière, Antoine. "Morphisms of Drinfeld Modules and their Algorithms." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0109.

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Nous nous intéressons à l'algorithmique des modules de Drinfeld, visant des applications au calcul formel et à la cryptographie. Les modules de Drinfeld sont aux corps de fonctions ce que les courbes elliptiques sont aux corps de nombres. Nous proposons trois contributions principales : - Le calcul efficace de polynômes caractéristiques d'endomorphismes et de normes d'isogénies de modules de Drinfeld. Nos algorithmes sont basés sur la correspondance entre les modules de Drinfeld et les motifs d'Anderson. Dans le cas de l'endomorphisme de Frobénius, nous décrivons un autre algorithme, basé sur
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Randrianarisoa, Tovohery Hajatiana. "Drinfeld modules and their application to factor polynomials." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71872.

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Thesis (MSc)--Stellenbosch University, 2012.<br>ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While an algorithm has been discovered to factor integers using elliptic curves, the discovery of Drinfeld modules, which are analogous to elliptic curves, made it possible to exhibit an algorithm for factorising polynomials in the ring Fq[T]. In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate the analogy between Drinfeld modules and Elliptic
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Thiéry, Alain. "Problemes d'independance algebrique pour les modules de drinfeld." Caen, 1992. http://www.theses.fr/1992CAEN2028.

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On sait depuis drinfeld qu'il existe, en caracteristique non nulle, une bijection entre les reseaux de rang fini et certains morphismes d'anneaux a valeurs dans les polynomes additifs. Cette bijection peut en fait etre consideree comme la restriction d'une bijection entre les reseaux, sans condition de rang, et certains morphismes a valeurs dans les series entieres additives. Dans le cas de rang fini, les fonctions exponentielles de drinfeld se comportent de facon analogue a la fonction exponentielle classique ou aux fonctions elliptiques de weierstrass. On peut ainsi montrer un analogue du th
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Bosser, Vincent. "Transcendance et approximation diophantienne sur les modules de drinfeld." Paris 6, 2000. http://www.theses.fr/2000PA066061.

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Cette these, qui traite d'approximation diophantienne sur les modules de drinfeld, comporte deux parties independantes. La premiere partie (chapitre i) a pour but d'etablir une minoration de formes lineaires de logarithmes dans le cas d'un produit de modules de drinfeld. Le resultat obtenu est d'une precision analogue a celle de la meilleure minoration connue dans le cas complexe. La seconde partie (chapitres ii a v) etablit successivement differents resultats d'approximation diophantienne, dans le but ultime d'etablir un analogue de la conjecture de bogomolov pour un produit de modules de dri
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Books on the topic "Modules de Drinfeld"

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Papikian, Mihran. Drinfeld Modules. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-19707-9.

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Genestier, Alain. Espaces symétriques de Drinfeld. Société Mathématique de France, 1996.

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Genestier, Alain. Espaces symétriques de Drinfeld. Société mathématique de France, 1996.

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Shnider, S. Quantum groups: From coalgebras to Drinfeld algebras : a guided tour. International Press, 1997.

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Shlomo, Sternberg, ed. Quantum groups: From coalgebras to Drinfeld algebras : a guided tour. International Press, 1993.

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Laumon, Gérard. Cohomology of Drinfeld modular varieties. Cambridge University Press, 1996.

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S, Kumar. Vector bundles on curves--new directions: Lectures given at the 3rd session of the Centro internazionale matematico estivo (C.I.M.E.) held in Cetraro (Cosenza), Italy, June 19-27, 1995. Edited by Laumon Gérard, Stuhler U, Narasimhan M. S, and Centro internazionale matematico estivo. Springer, 1997.

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Flicker, Yuval Z. Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications. Springer New York, 2013.

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Alain, Genestier, Lafforgue Vincent, and SpringerLink (Online service), eds. L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld. Birkhäuser, 2008.

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David, Goss. Basic structures of function field arithmetic. Springer, 1998.

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Book chapters on the topic "Modules de Drinfeld"

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Goss, David. "Drinfeld Modules." In Basic Structures of Function Field Arithmetic. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-61480-4_4.

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Hurt, Norman E. "Drinfeld Modules." In Many Rational Points. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0251-5_5.

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Gekeler, Ernst-Ulrich. "Drinfeld modules." In Drinfeld Modular Curves. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0072694.

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Papikian, Mihran. "Drinfeld Modules over Local Fields." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_6.

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Papikian, Mihran. "Analytic Theory of Drinfeld Modules." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_5.

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Papikian, Mihran. "Non-Archimedean Fields." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_2.

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Papikian, Mihran. "Drinfeld Modules Over Global Fields." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_7.

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Papikian, Mihran. "Basic Properties of Drinfeld Modules." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_3.

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Papikian, Mihran. "Drinfeld Modules over Finite Fields." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_4.

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Papikian, Mihran. "Algebraic Preliminaries." In Drinfeld Modules. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19707-9_1.

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Conference papers on the topic "Modules de Drinfeld"

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Gekeler, E. U., M. van der Put, M. Reversat, and J. Van Geel. "Drinfeld Modules, Modular Schemes and Applications." In Workshop. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789814529990.

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Gekeler, Ernst-Ulrich. "Drinfeld modules and local fields of positive characteristic." In Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.239.

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Musleh, Yossef, and Éric Schost. "Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module." In ISSAC '19: International Symposium on Symbolic and Algebraic Computation. ACM, 2019. http://dx.doi.org/10.1145/3326229.3326256.

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Coquereaux, Robert. "Character tables (modular data) for Drinfeld doubles of finite groups." In 7th International Conference on Mathematical Methods in Physics. Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.175.0024.

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Musleh, Yossef, and Éric Schost. "Computing the Characteristic Polynomial of Endomorphisms of a finite Drinfeld Module using Crystalline Cohomology." In ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023. ACM, 2023. http://dx.doi.org/10.1145/3597066.3597080.

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