Abelian varieties isogenous to a power of an elliptic curve
Author(s)Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T.; ... Show more Show less
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Let be an elliptic curve over a field k. Let [mathematical notation] . There is a functor [mathematical notation] 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 Hom (-, E) in the opposite direction. We prove necessary and sufficient conditions on 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 F[subscript P].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Jordan, Bruce W. et al. "Abelian varieties isogenous to a power of an elliptic curve." Compositio Mathematica 154, 5 (March 2018): 934-959 © 2018 The Authors