Lattices in Tate modules

Refining a theorem of Zarhin, we prove that, given a g-dimensional abelian variety X and an endomorphism u of X, 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 u is given by A, and similarly for the cova...

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Detalles Bibliográficos
Autores principales: Poonen, Bjorn, Rybakov, Sergey
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2021
Materias:
Physical Sciences
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8670492/
https://www.ncbi.nlm.nih.gov/pubmed/34848540
http://dx.doi.org/10.1073/pnas.2113201118
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author Poonen, Bjorn
Rybakov, Sergey
author_facet Poonen, Bjorn
Rybakov, Sergey
author_sort Poonen, Bjorn
collection PubMed
description Refining a theorem of Zarhin, we prove that, given a g-dimensional abelian variety X and an endomorphism u of X, 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 u is given by A, and similarly for the covariant Dieudonné module if over a perfect field of characteristic p.
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spelling pubmed-86704922021-12-28 Lattices in Tate modules Poonen, Bjorn Rybakov, Sergey Proc Natl Acad Sci U S A Physical Sciences Refining a theorem of Zarhin, we prove that, given a g-dimensional abelian variety X and an endomorphism u of X, 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 u is given by A, and similarly for the covariant Dieudonné module if over a perfect field of characteristic p. National Academy of Sciences 2021-11-30 2021-12-07 /pmc/articles/PMC8670492/ /pubmed/34848540 http://dx.doi.org/10.1073/pnas.2113201118 Text en Copyright © 2021 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by/4.0/This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY) (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Physical Sciences
Poonen, Bjorn
Rybakov, Sergey
Lattices in Tate modules
title Lattices in Tate modules
title_full Lattices in Tate modules
title_fullStr Lattices in Tate modules
title_full_unstemmed Lattices in Tate modules
title_short Lattices in Tate modules
title_sort lattices in tate modules
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8670492/
https://www.ncbi.nlm.nih.gov/pubmed/34848540
http://dx.doi.org/10.1073/pnas.2113201118
work_keys_str_mv AT poonenbjorn latticesintatemodules
AT rybakovsergey latticesintatemodules

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