Irreduzible Komponenten von 2-adischen Deformationsr\"aumen

TL;DR

This paper proves a bijection between irreducible components of certain 2-adic deformation spaces and their determinants, confirming a conjecture in Galois representation theory.

Contribution

It establishes a natural correspondence between irreducible components of 2-adic deformation spaces and their determinants, advancing understanding of Galois deformation rings.

Findings

Confirmed conjecture of B"ockle--Juschka

Established bijection between deformation components and determinants

Enhanced understanding of 2-adic Galois representations

Abstract

We prove that the irreducible components of the space of framed deformations of a $2$-dimensional mod $2$ representation with scalar semi-simplification of the absolute Galois group of $\mathbb{Q}_2$ are in natural bijection with those of its determinant, confirming a conjecture of B\"ockle--Juschka