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

@article{Baldi2018OnTG,
  title={On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties},
  author={G. Baldi},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
  • G. Baldi
  • Published 2018
  • Mathematics
  • arXiv: Algebraic Geometry
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… Expand
Categoricity of Shimura Varieties
We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity.
Finite descent obstruction for Hilbert modular varieties
Abstract Let S be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of $\mathbb {Z}_{S}$ -points on integral models ofExpand

References

SHOWING 1-10 OF 23 REFERENCES
INTEGRAL AND ADELIC ASPECTS OF THE MUMFORD–TATE CONJECTURE
Let $Y$ be an abelian variety over a subfield $k\subset \mathbb{C}$ that is of finite type over $\mathbb{Q}$. We prove that if the Mumford–Tate conjecture for $Y$ is true, then also some refinedExpand
Galois-generic points on Shimura varieties
We discuss existence and abundance of Galois-generic points for adelic representations attached to Shimura varieties. First, we show that, for Shimura varieties of abelian type, l-Galois-genericExpand
Congruence Properties of Zariski‐Dense Subgroups I
This paper deals with the following general situation: we are given an algebraic group G defined over a number field K, and a subgroup F of the group G(K) of K-rational points of G. Then what shouldExpand
Linearity properties of Shimura varieties, II
Let A=Ag, 1, n denote the moduli scheme over Z[1/N] of p.p. g-dimensional abelian varieties with a level n structure; its generic fibre can be described as a Shimura variety. We study its ‘ShimuraExpand
An Open Adelic Image Theorem for Abelian Schemes
In this note, we prove an adelic open image theorem for abelian schemes and, more generally, families of 1-motives. This result, which can be interpreted as an adelic specialization theorem, showsExpand
Automorphic Representations, Shimura Varieties, and Motives. Ein Marchen*
1. Introduction. It had been my intention to survey the problems posed by the study of zetafunctions of Shimura varieties. But I was too sanguine. This would be a mammoth task, and limitations ofExpand
Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part
© Foundation Compositio Mathematica, 1992, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditionsExpand
Mumford–Tate and generalised Shafarevich conjectures
In this paper, we formulate the generalised Isogeny, Mumford–Tate and Shafarevich conjectures and prove that they are equivalent.RésuméDans cet article, nous formulons les conjectures généraliséesExpand
La conjecture de Weil pour les surfacesK3
1. Enonc6 du th~or~me Soient Fq un corps ~t q ~l~ments, Fq une cl6ture alg6brique de Fq, r la substitution de Frobenius xv-~x q et F= tp -1 le << Frobenius g6om6trique >>. Soit X un sch6ma (s6par6 deExpand
2 ,
Since 2001, we have observed the central region of our Galaxy with the near-infrared (J, H, and Ks) camera SIRIUS and the 1.4 m telescope IRSF. Here I present the results about the infraredExpand
...
1
2
3
...