The Scholze-Weinstein conjecture on local models

Abstract: Inspired by the theory of local models of Shimura varieties, Scholze-Weinstein proposed a conjecture predicting representability of certain minuscule closed sub-v-sheaves of their p-adic de Rham affine Grassmannian by a projective flat and geometrically reduced normal scheme.

In my talk, I'll explain the motivation behind the problem stemming from Shimura varieties, review the necessary technical background and ultimately sketch a proof for pseudo-tame groups without exceptional factors. To achieve this, I'll determine the Picard group of the Witt vectors affine Grassmannian as conjectured by Bhatt-Scholze. Time permitting, I might outline a (very much incomplete) strategy for handling exceptional groups.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html