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On compatibility of the $\ell$-adic realisations of an abelian motive. (arXiv:1706.09444v1 [math.AG])
来源于:arXiv
In this article we introduce the notion of a quasi-compatible system of
Galois representations. The quasi-compatibility condition is a slight
relaxation of the classical compatibility condition in the sense of Serre. The
main theorem that we prove is the following: Let $M$ be an abelian motive, in
the sense of Yves Andr\'e. Then the $\ell$-adic realisations of $M$ form a
quasi-compatible system of Galois representations. (In fact, we actually prove
something stronger. See theorem 5.1.) As an application, we deduce that the
absolute rank of the $\ell$-adic monodromy groups of $M$ does not depend on
$\ell$. In particular, the Mumford-Tate conjecture for $M$ does not depend on
$\ell$. 查看全文>>