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arXiv · 2201.01234

On the $p$-adic theory of local models

Johannes Anschütz·Ian Gleason·João Lourenço·Timo Richarz
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Abstract

We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as the test function conjecture of Haines--Kottwitz in this framework. To this end, we establish a specialization principle for well-behaved $p$-adic kimberlites, show that these include the v-sheaf local models, determine their special fibers using hyperbolic localization for the \'etale cohomology of small v-stacks, and analyze the resulting specialization morphism using convolution.

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Johannes Anschütz, Ian Gleason, João Lourenço, Timo Richarz. 2022-01-04. On the $p$-adic theory of local models. https://arxiv.org/abs/2201.01234

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