Galois cohomology of a $p$-adic field via $(Φ,Γ)$-modules in the imperfect residue field case

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159512For 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 $(Φ,Γ)$-modules. We shall generalize his work to the imperfect residue field (the residue field has a finite $p$-basis) case.18 pages, LaTeX, to appear in J. Math. Sci. Univ. TokyoNumber Theory11F30; 13K05Galois cohomology of a $p$-adic field via $(Φ,Γ)$-modules in the imperfect residue field casetext