scholarly journals Examples of abelian surfaces failing the local–global principle for isogenies

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
Barinder S. Banwait
Keyword(s):  
Abelian Surfaces ◽  
Global Principle

On the computation of the endomorphism rings of abelian surfaces

2021 ◽  
Author(s):  
Claus Fieker ◽  
Tommy Hofmann ◽  
Sogo Pierre Sanon
Keyword(s):  
Abelian Surfaces ◽  
Endomorphism Rings

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.

scholarly journals Principally polarizable isogeny classes of abelian surfaces over finite fields

2008 ◽  
Vol 15 (1) ◽  
pp. 121-127 ◽  
Author(s):  
Everett W. Howe ◽  
Daniel Maisner ◽  
Enric Nart ◽  
Christophe Ritzenthaler
Keyword(s):  
Finite Fields ◽  
Abelian Surfaces
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