Lattices in Tate modules.
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- Record sourced from PubMed, PMID 34848540.
- Also identified by DOI 10.1073/pnas.2113201118 and PMC identifier 8670492.
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Abstract
Refining a theorem of Zarhin, we prove that, given a <i>g</i>-dimensional abelian variety <i>X</i> and an endomorphism <i>u</i> of <i>X</i>, 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 <i>u</i> is given by <i>A</i>, and similarly for the covariant Dieudonné module if over a perfect field of characteristic <i>p</i>.