On the geometric connected components of moduli of mixed characteristic shtukas

Abstract: By a theorem of Scholze and Weinstein, moduli spaces of mixed characteristic shtukas generalize Rapoport-Zink spaces at infinite level. In this talk, we describe the structure of the set of geometric connected components of those moduli spaces that are associated to the data $(G,b,\mu)$ with $G$ an unramified reductive group and $(b,\mu)$ HN-irreducible. This result generalizes the work of Chen on the geometric connected components of unramified HN-irreducible Rapoport-Zink spaces of EL and PEL type. In the interest of time, we only sketch the part of the proof that requires a new geometric ingredient: namely, the specialization map for Scholze's category of diamonds.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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