On the p-adic theory of local models

2022/01/04 by Anschütz, Johannes, Gleason, Ian, Lourenço, João +1 · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.01234

Abstract

We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models of local Shimura varieties and the test function conjecture of Haines--Kottwitz in this setting. In order to achieve this, we establish the 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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• Dual Shellability of Admissible Set and Cohen-Macaulayness of Local Models
• Multimodal Representation Learning and Fusion

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