CaltechAUTHORS
Published May 2018 | Version Submitted
Journal Article Open

Abelian varieties isogenous to a power of an elliptic curve

Creators

  • 1. ROR icon Baruch College
  • 2. ROR icon Massachusetts Institute of Technology
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon King's College London
  • 5. ROR icon Harvard University

Abstract

Let E be an elliptic curve over a field k. Let R:=End E. There is a functor Hom_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 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 F_p.

Additional Information

© The Authors 2018. Published online: 21 March 2018. B.P. was supported in part by National Science Foundation grant DMS-1069236 and DMS-1601946 and grants from the Simons Foundation (#340694 and #402472 to Bjorn Poonen). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Simons Foundation. It is a pleasure to thank Everett Howe, Tony Scholl, and Christopher Skinner for helpful discussions. We thank also the referees for valuable suggestions on the exposition.

Attached Files

Submitted - 1602.06237.pdf

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1602.06237.pdf

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Additional details

Identifiers

Eprint ID
81760
Resolver ID
CaltechAUTHORS:20170922-140322875

Related works

Describes
https://arxiv.org/abs/1602.06237 (URL)

Funding

NSF
DMS-1069236
NSF
DMS-1601946
Simons Foundation
340694
Simons Foundation
402472

Dates

Created
2017-09-22
Created from EPrint's datestamp field
Updated
2021-11-15
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Mathematics Department