On 2-dimensional 2-adic Galois representations of local and global fields

Abstract

We describe the generic blocks in the category of smooth locally admissible mod $2$ representations of ${\mathrm{GL}}_2({\mathbb{Q}}_2)$. As an application we obtain new cases of Breuil--Mézard and Fontaine--Mazur conjectures for $2$-dimensional $2$-adic Galois representations.

46 pages, minor changes

Cited by in corpus (4)

• Patching and the p-adic Langlands program for GL(2, Q_p)
• On the modularity of 2-adic potentially semi-stable deformation rings
• On the Breuil-Schneider conjecture: Generic case
• On the locus of $2$-dimensional crystalline representations with a given reduction modulo $p$