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arXiv · 2405.12392

Integral canonical models of exceptional Shimura varieties

Benjamin Bakker·Ananth N Shankar·Jacob Tsimerman
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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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Benjamin Bakker, Ananth N Shankar, Jacob Tsimerman. 2024-05-20. Integral canonical models of exceptional Shimura varieties. https://arxiv.org/abs/2405.12392

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