Lattices in Tate modules
| Autor: | Bjorn Poonen, Sergey Rybakov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Abelian variety
Pure mathematics Multidisciplinary Endomorphism Mathematics - Number Theory abelian variety Tate module Basis (universal algebra) Matrix (mathematics) Mathematics - Algebraic Geometry Dieudonné module Physical Sciences FOS: Mathematics Perfect field endomorphism Covariant transformation Number Theory (math.NT) Algebraic Geometry (math.AG) 14K02 (Primary) 14K05 (Secondary) Mathematics |
| Zdroj: | Proceedings of the National Academy of Sciences of the United States of America |
| Popis: | 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 $A \in \operatorname{M}_{2g}(\mathbb{Z})$ such that each Tate module $T_\ell X$ has a $\mathbb{Z}_\ell$-basis on which the action of $u$ is given by $A$. 3 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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