Author:
Jordan Bruce W.,Keeton Allan G.,Poonen Bjorn,Rains Eric M.,Shepherd-Barron Nicholas,Tate John T.
Abstract
Let $E$ be an elliptic curve over a field $k$. Let $R:=\operatorname{End}E$. There is a functor $\mathscr{H}\!\mathit{om}_{R}(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a power of $E$, and a functor $\operatorname{Hom}(-,E)$ in the opposite direction. We prove necessary and sufficient conditions on $E$ for these functors to be equivalences of categories. We also prove a partial generalization in which $E$ is replaced by a suitable higher-dimensional abelian variety over $\mathbb{F}_{p}$.
Subject
Algebra and Number Theory
Reference31 articles.
1. Endomorphisms of abelian varieties over finite fields
2. Produkte abelscher Varietäten und Moduln über Ordnungen;Schoen;J. Reine Angew. Math.,1992
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献