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

2025/08/15 by Howe, Sean
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.11595

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.

Citations

• Inscription, twistors, and p-adic periods
• Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice
• Admissible pairs and p-adic Hodge structures II: The bi-analytic Ax-Lindemann theorem
• Geometrization of the local Langlands correspondence
• The smooth locus in infinite-level Rapoport-Zink spaces
• Towards a theory of local Shimura varieties
• Moduli of p-divisible groups
• Semistable models for modular curves of arbitrary level

Related

• Convolution morphisms and Kottwitz conjecture
• Relative étale slices and cohomology of moduli spaces
• A note on the cohomology of moduli spaces of local shtukas
• On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties
• Moduli spaces of local G-shtukas