Components of moduli stacks of two-dimensional Galois representations

TL;DR

This paper investigates the structure of moduli stacks of two-dimensional Galois representations, revealing how their irreducible components are indexed by Serre weights, thus advancing understanding of p-adic Galois deformation theory.

Contribution

It provides a detailed analysis of the irreducible components of moduli stacks of Galois representations and connects these components to Serre weights, offering new insights into their structure.

Findings

Components are indexed by Serre weights.

Established a natural correspondence between components and weights.

Enhanced understanding of the geometry of Galois representation stacks.

Abstract

In a previous article we introduced various moduli stacks of two-dimensional tamely potentially Barsotti-Tate representations of the absolute Galois group of a p-adic local field, as well as related moduli stacks of Breuil-Kisin modules with descent data. We study the irreducible components of these stacks, establishing in particular that the components of the former are naturally indexed by certain Serre weights.