Work

Relative representability and parahoric level structures

Year: 2026

Type: article

Abstract: We establish a representability criterion of v -sheaf theoretic modifications of formal schemes and apply this criterion to moduli spaces of parahoric level structures on local shtukas. In the proof, we introduce nice classes of equivariant profinite perfectoid covers and study geometric quotients of perfectoid formal schemes by profinite groups. As a corollary, we show the local representability of integral models of local Shimura varieties under hyperspecial levels, and study the forgetful morphisms between integral models of Shimura varieties associated with inclusions of parahoric subgroups under hyperspecial levels.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03469-7

Author: Yuta Takaya

Institution: The University of Tokyo

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: University of Tokyo, Japan Society for the Promotion of Science, Division of Mathematical Sciences