Sakagaito, MakotoMakotoSakagaito2025-08-282025-08-282024-02-012331-842210.48550/arXiv.2402.18042http://repository.iitgn.ac.in/handle/IITG2025/20142Let n?0 be an integer. For a normal crossing variety Y over the spectrum of a field k of positive characteristic p>0, K.Sato defined an �tale logarithmic Hodge-Witt sheaf ?nY,r on the �tale site Ye�t which agrees with Wr?nY,log in the case where Y is smooth over Spec(k). In this paper, we prove the Gersten-type conjecture for ?nr over the henselization of the local ring OY,y of Y at a point y?Y. As an application, we prove the relative version of the Gersten-type conjecture for the p-adic �tale Tate twist T1(n) over the henselization of the local ring OX,x of a semistable family X over the spectrum of a discrete valuation ring B of mixed characteristic (0,p) at a point x?X in the case where B contains p-th roots of unity. Moreover, we prove a generalization of Artin's theorem about the Brauer groups.en-USe-Print123456789/555