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On matrices of endomorphisms of abelian varieties
Yuri G. Zarhin1
1 Pennsylvania State University, Department of Mathematics, University Park, PA 16802, USA
Mathematics Research Reports, Volume 1 (2020), pp. 55-68.

We study endomorphisms of abelian varieties and their action on the ℓ-adic Tate modules. We prove that for every endomorphism one may choose a basis of each ℚ ℓ -Tate module such that the corresponding matrix has rational entries and does not depend on ℓ.

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Accepted:
Published online:
DOI: 10.5802/mrr.5
Classification: 14K05, 16K20
Keywords: Abelian varieties, Tate modules, Semisimple algebras
Yuri G. Zarhin 1

1 Pennsylvania State University, Department of Mathematics, University Park, PA 16802, USA 
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Yuri G. Zarhin. On matrices of endomorphisms of abelian varieties. Mathematics Research Reports, Volume 1 (2020), pp. 55-68. doi : 10.5802/mrr.5. https://mrr.centre-mersenne.org/articles/10.5802/mrr.5/

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