Lattices in Tate modules

Lattices in Tate modules

Refining a theorem of Zarhin, we prove that, given a -dimensional abelian variety and an endomorphism of , there exists a matrix [Formula: see text] such that each Tate module [Formula: see text] has a [Formula: see text]-basis on which the action of is given by , and similarly for the covariant Die...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2021-12, Vol.118 (49), Article Paper No. e2113201118, 3
Main Authors: Poonen, Bjorn, Rybakov, Sergey
Format: Article
Language:eng
Subjects:
Lattices
Modules
Physical Sciences
Online Access:Get full text
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Summary:Refining a theorem of Zarhin, we prove that, given a -dimensional abelian variety and an endomorphism of , there exists a matrix [Formula: see text] such that each Tate module [Formula: see text] has a [Formula: see text]-basis on which the action of is given by , and similarly for the covariant Dieudonné module if over a perfect field of characteristic .
ISSN:0027-8424
1091-6490