Abelian varieties isogenous to a power of an elliptic curve
Name
1602.06237.pdf
Description
Submitted version
Size
361.45 KB
Format
Adobe PDF
Checksum (MD5)
dd1803b90d5dc7868eb46a6cff86885a
Author(s)
Jordan, Bruce W.
Keeton, Allan G.
Poonen, Bjorn
Rains, Eric M.
Shepherd-Barron, Nicholas
Tate, John T.
Date Issued
March 2018
Journal
Compositio Mathematica
Publisher
Wiley
Citation
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
Version
Original manuscript
Abstract
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].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/s0010437x17007990
