ON ÉTALE HYPERCOHOMOLOGY OF HENSELIAN REGULAR LOCAL RINGS WITH VALUES IN p-ADIC ÉTALE TATE TWISTS

Let R be the henselization of a local ring of a semistable family over the spectrum of a discrete valuation ring of mixed characteristic (0, p) and k the residue field of R. In this paper, we prove an isomorphism of étale hypercohomology groups (Formula presented) for any integers n ≽ 0 and r > 0 where (Formula presented) is the p-adic Tate twist and W<inf>r</inf>Ωⁿ<inf>log</inf> is the logarithmic Hodge-Witt sheaf. As an application, we prove the local-global principle for Galois cohomology groups over function fields of curves over an excellent henselian discrete valuation ring of mixed characteristic.