A cohomological smoothness conjecture for moduli of mixed characteristic local shtukas with one leg

TL;DR

This paper characterizes the smooth locus of moduli spaces of mixed characteristic local shtukas and proves cohomological smoothness in certain cases, extending previous results to more general settings.

Contribution

It provides a geometric criterion for smoothness and proves cohomological smoothness for EL Rapoport--Zink spaces, generalizing earlier work.

Findings

Characterization of the smooth locus via tangent spaces

Proof of cohomological smoothness for EL Rapoport--Zink spaces

Extension of previous results to more general moduli spaces

Abstract

We give a simple geometric characterization of the locus where the inscribed Banach--Colmez Tangent Spaces of moduli of mixed characteristic local shtukas with one leg and fixed determinant are connected. We conjecture that the structure morphism for the underlying diamond is cohomologically smooth over this locus and, applying the Fargues--Scholze Jacobian criterion, we prove this conjecture in the case of EL infinite level Rapoport--Zink spaces, generalizing a result of Ivanov--Weinstein in the basic case.