## Galois cohomology of a $p$-adic field via $(\Phi,\Gamma)$-modules in the imperfect residue field case

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 2, Page 219--241.

Morita, Kazuma
Galois cohomology of a $p$-adic field via $(\Phi,\Gamma)$-modules in the imperfect residue field case
For a $p$-adic local field $K$ with perfect residue field, L. Herr constructed a complex which computes the Galois cohomology of a $p$-torsion representation of the absolute Galois group of $K$ by using the theory of $(\Phi,\Gamma)$-modules. We shall generalize his work to the imperfect residue field (the residue field has a finite $p$-basis) case.
Keywords: Galois cohomology, ($\Phi,\Gamma$)-modules.