#### Vol. 10, No. 6, 2016

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

### Vytautas Paškūnas

Vol. 10 (2016), No. 6, 1301–1358
##### Abstract

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

##### Keywords
$p$-adic Langlands, Fontaine–Mazur, modularity lifting
Primary: 11F80