On the geometric MumfordTate conjecture for subvarieties of Shimura varieties
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 MumfordTate conjecture.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.04682
 Bibcode:
 2018arXiv180204682B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory
 EPrint:
 Accepted for publication in Proceedings of the American Mathematical Society