Galois cohomology of $p$-adic fields and $(\phi ,\tau )$-modules

Abstract

We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, using the associated $(\phi ,\tau )$-modules (defined by Xavier Caruso), instead of $(\phi ,\Gamma )$-modules. We also give an application to $p$-divisible groups.

111 pages