Integral canonical models of exceptional Shimura varieties
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.
Keywords
Cite
@article{arxiv.2405.12392,
title = {Integral canonical models of exceptional Shimura varieties},
author = {Benjamin Bakker and Ananth N Shankar and Jacob Tsimerman},
journal= {arXiv preprint arXiv:2405.12392},
year = {2025}
}
Comments
37 pages. We have corrected an error in the proof of the main theorem, which did not account for multiple fibers. We now use extension results of Fontaine-Lafaille modules. Notably, we use Falting's theory of Fontaine-Lafaille modules over ramified rings of integers. The results are unchanged, except we can no longer prove the (unramified) Borel extension result. Comments welcome!