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∈M2g(ℤ) such that each Tate module TℓX has a ℤℓ-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.

中文翻译：

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Tate 模块中的晶格 [数学]

精炼Zarhin的定理，我们证明了，给定摹维阿贝尔品种X和同态ü的X，存在矩阵一个∈米2G(ℤ) 使得每个 Tate 模块 吨ℓX 有一个 ℤℓ- u的作用由A给出的基础，对于协变 Dieudonné 模块，如果在特征p的完美域上，则类似。