Moduli stacks of two-dimensional Galois representations

TL;DR

This paper constructs moduli stacks for two-dimensional Galois representations over p-adic fields and links their geometric properties to Serre's conjecture, advancing understanding of Galois deformation theory.

Contribution

It introduces a geometric framework for mod p Galois representations and connects it to the weight part of Serre's conjecture for GL(2).

Findings

Established moduli stacks for 2D Galois representations.

Connected stack geometry to Serre's conjecture.

Provided new insights into Galois deformation spaces.

Abstract

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).