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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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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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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].
Date issued
2018-03
URI
https://hdl.handle.net/1721.1/126479
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
0010-437X
1570-5846

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