Integral canonical models of exceptional Shimura varieties

2024/05/20 by Benjamin Bakker, Bakker, Benjamin, Ananth N. Shankar +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.12392

Abstract

We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of integral canonical models for images of period maps corresponding to geometric families. We deduce several consequences from this, including an unramified rigid analogue of Borel's extension theorem, a version of Tate semisimplicity, CM lifting theorems, and a weakened version of Tate's isogeny theorem for ordinary points.

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• Finiteness of function field-valued points on exceptional Shimura varieties
• G-companions on algebraic stacks and applications to canonical ℓ-adic local systems on Shimura stacks

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