The higher direct images of locally constant group schemes from the Kummer log flat topology to the classical flat topology

Abstract Let S be a fine and saturated (fs) log scheme, and let F be a group scheme over the underlying scheme of S which is étale locally representable by (1) a finite dimensional $\mathbb{Q}$ -vector space, or (2) a finite rank free abelian group, or (3) a finite abelian group. We give a full description of all the higher direct images of F from the Kummer log flat site to the classical flat site. In particular, we show that: in case (1) the higher direct images of F vanish; and in case (2) the first higher direct image of F vanishes and the n th ( $n\gt 1$ ) higher direct image of F is isomorphic to the $(n-1)$ -th higher direct image of $F\otimes_{{\mathbb Z}}{\mathbb Q}/{\mathbb Z}$ . In the end, we make some computations when the base is a standard henselian log trait or a Dedekind scheme endowed with the log structure associated to a finite set of closed points.