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

2018/02/13 by Gregorio Baldi, Baldi, Gregorio
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.04682

openalex publication_date 2018/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the image of \ℓ-adic representations attached to subvarieties of\nShimura varieties Sh_K(G,X) that are not contained in a smaller Shimura\nsubvariety and have no isotrivial components. We show that, for \ℓ large\nenough (depending on the Shimura datum (G,X) and the subvariety), such image\ncontains the \ℤ_\ℓ-points coming from the simply connected cover of\nthe derived subgroup of G. This can be regarded as a geometric version of the\nintegral \ℓ-adic Mumford-Tate conjecture.\n

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