Cohomology and Duality for (phi,Gamma)-modules over the Robba ring

Details Cohomology and Duality for (phi,Gamma)-modules over the Robba ring Cohomology and Duality for (phi,Gamma)-modules over the Robba ring

2007-11-27

arxiv.org/abs/0711.4346v2

Int Math Res Notices, 2007 Volume 2007: article ID rnm150

Mathematics

Number Theory

27 pages. Final version

Scientific paper

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily etale (phi,Gamma)-modules over the Robba ring, of the Euler-Poincare characteristic formula and Tate local duality for p-adic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations.

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