Deformation theory of mixed-characteristic shtukas

Abstract: The deformations of a given $p$-divisible group can be understood through Grothendieck--Messing theory. The problem of generalizing the theory to groups other than $\mathcal{G} = \mathrm{GL}_n$ has been studied by Faltings, Kisin, Bültel--Pappas, Kisin--Pappas--Zhou, Pappas--Rapoport, Hoff, Ito, etc. In this talk I will work in the Scholze--Weinstein setting of mixed characteristic shtukas and describe a deformation theory of $\mathcal{G}$-shtukas with one leg bounded by $\mu$, relative to the local model. The theory, which is inspired by Faltings' explicit deformation theory, works uniformly for general parahoric group schemes $\mathcal{G}/\mathbb{Z}_p$ and minuscule cocharacters $\mu$ of the geometric generic fiber.

number theory

Audience: researchers in the topic

London number theory seminar

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