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arXiv · 1802.04682

On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties

Gregorio Baldi
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Abstract

We study the image of $\ell$-adic representations attached to subvarieties of Shimura varieties $Sh_K(G,X)$ that are not contained in a smaller Shimura subvariety and have no isotrivial components. We show that, for $\ell$ large enough (depending on the Shimura datum $(G,X)$ and the subvariety), such image contains the $\mathbb{Z}_\ell$-points coming from the simply connected cover of the derived subgroup of $G$. This can be regarded as a geometric version of the integral $\ell$-adic Mumford-Tate conjecture.

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Gregorio Baldi. 2018-02-13. On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties. https://arxiv.org/abs/1802.04682

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