G-valued crystalline representations with minuscule p-adic Hodge type

Abstract

We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type with the connected components of moduli of "finite flat models with G-structure." The main ingredients are a construction in integral p-adic Hodge theory using Liu's theory of $(\phi ,\hat{G})$-modules and the local models constructed by Pappas and Zhu.

References in corpus (5)

• Local models of Shimura varieties, I. Geometry and combinatorics
• Local models for Weil-restricted groups
• $p$-adic Hodge theory in rigid analytic families
• Some Bounds for ramification of $p^n$-torsion semi-stable representations
• G-torsors over a Dedekind scheme

Cited by in corpus (4)

• A Harder-Narasimhan theory for Kisin modules
• Prismatic $G$-displays and descent theory
• A note on crystalline liftings in the ${\mathbb{Q}}_p$ case
• Crystalline liftings and weight part of Serre's conjecture