scholarly journals Finiteness theorems for potentially equivalent Galois representations: Extension of Faltings’ finiteness criteria

2021 ◽  
Author(s):  
Plawan Das ◽  
Conjeeveram Rajan
Keyword(s):  
Galois Representations ◽  
Finiteness Theorems

Galois Representations and (Phi, Gamma)-Modules

2017 ◽  
Author(s):  
Peter Schneider
Keyword(s):  
Galois Representations

Elliptic Curves and Big Galois Representations

2008 ◽  
Author(s):  
Daniel Delbourgo
Keyword(s):  
Elliptic Curves ◽  
Galois Representations

scholarly journals Selmer groups of symmetric powers of ordinary modular Galois representations

2021 ◽  
Vol 143 (1) ◽  
pp. 125-173
Author(s):  
Xiaoyu Zhang
Keyword(s):  
Galois Representations ◽  
Selmer Groups ◽  
Symmetric Powers

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

Galois representations and Hecke operators associated with the mod- $p$ cohomology of $GL(m(p-1),\mathbb{Z})$

1998 ◽  
Vol 227 (4) ◽  
pp. 685-703 ◽  
Author(s):  
Avner Ash ◽  
Rajesh Manjrekar
Keyword(s):  
Galois Representations ◽  
Hecke Operators ◽  
Mod P

scholarly journals Finiteness theorems for the shifted Witt and higher Grothendieck–Witt groups of arithmetic schemes

2012 ◽  
Vol 351 (1) ◽  
pp. 254-278 ◽  
Author(s):  
Jeremy Jacobson
Keyword(s):  
Finiteness Theorems ◽  
Witt Groups

Computing Galois representations of modular abelian surfaces

2014 ◽  
Vol 17 (A) ◽  
pp. 36-48 ◽  
Author(s):  
Jinxiang Zeng
Keyword(s):  
Abelian Variety ◽  
Efficient Algorithm ◽  
Galois Representations ◽  
Abelian Surfaces ◽  
Genus Two

AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f\in S_2(\Gamma _0(N))$ be a normalized newform such that the abelian variety $A_f$ attached by Shimura to $f$ is the Jacobian of a genus-two curve. We give an efficient algorithm for computing Galois representations associated to such newforms.

Galois representations for holomorphic Siegel modular forms

2012 ◽  
Vol 355 (1) ◽  
pp. 381-400 ◽  
Author(s):  
Andrei Jorza
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Siegel Modular Forms

Galois representations, Mumford-Tate groups and good reduction of abelian varieties

2004 ◽  
Vol 329 (1) ◽  
pp. 119-160 ◽  
Author(s):  
Frédéric Paugam
Keyword(s):  
Galois Representations ◽  
Abelian Varieties ◽  
Good Reduction
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