Hodge cohomology on blow‐ups along subvarieties

Abstract

AbstractWe establish a blow‐up formula for Hodge cohomology of locally free sheaves on smooth proper varieties over an algebraically closed field of positive characteristic. For this, we introduce a notion of relative Hodge sheaves and study their behavior under blow‐ups along smooth centers. In particular, as an application, we study the blow‐up invariance of the E2‐degeneracy of the Hochschild–Kostant–Rosenberg spectral sequence for smooth proper varieties.