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arxiv: 1509.00332 · v2 · pith:WEZRHKCTnew · submitted 2015-09-01 · 🧮 math.NT

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

classification 🧮 math.NT
keywords representationsadicdimensionalgaloisadmissibleapplicationblocksbreuil--m
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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--M\'ezard and Fontaine--Mazur conjectures for $2$-dimensional $2$-adic Galois representations.

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