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We prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in irreducible admissible unitary p-adic Banach space representations of GL2(Q
) with p≥5. This enables us to restate nicely the p-adic local Langlands correspondence for GL2(Q...
We prove that in the category of pro-p groups any finitely generated group G with a free open subgroup splits either as an amalgamated free product or as an HNN-extension over a finite p-group. From this result we deduce that such a pro-p group is the pro-p completion of a fundamental group of a...
We construct a representation of the affine W-algebra of
on the equivariant homology space of the moduli space of U
-instantons, and we identify the corresponding module. As a corollary, we give a proof of a version of the AGT conjecture concerning pure N=2...
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