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

preprint2016arXivOpen access

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.

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

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