We study endomorphisms of abelian varieties and their action on the -adic Tate modules. We prove that for every endomorphism one may choose a basis of each -Tate module such that the corresponding matrix has rational entries and does not depend on .
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Mots clés : Abelian varieties, Tate modules, Semisimple algebras
@article{MRR_2020__1__55_0, author = {Zarhin, Yuri G.}, title = {On matrices of endomorphisms of abelian varieties}, journal = {Mathematics Research Reports}, pages = {55--68}, publisher = {MathOA foundation}, volume = {1}, year = {2020}, doi = {10.5802/mrr.5}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/mrr.5/} }
Zarhin, Yuri G. On matrices of endomorphisms of abelian varieties. Mathematics Research Reports, Tome 1 (2020), pp. 55-68. doi : 10.5802/mrr.5. http://archive.numdam.org/articles/10.5802/mrr.5/
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