The topological Breuil-M\'ezard conjecture for classical groups

TL;DR

This paper advances the understanding of the topological Breuil-Mézard conjecture for classical groups by computing dimensions of Emerton-Gee stacks and describing their Chow groups, introducing a novel method for analyzing Galois cup products.

Contribution

It provides explicit dimension calculations and Chow group descriptions for Emerton-Gee stacks of classical groups, with a new approach to Galois cup product analysis.

Findings

Dimensions of Emerton-Gee stacks are computed for classical groups.

Explicit descriptions of top-dimensional Chow groups are provided.

Results are unconditional for p ≠ 2.

Abstract

For unitary, orthogonal and symplectic groups, we compute the dimension of the reduced Emerton-Gee stacks, and give an explicit description of their top-dimensional Chow group. Our results are unconditional when $p\neq 2$. The main innovation is a new method for analyzing the vanishing locus of Galois cup products valued in high dimensions.