Blow-up invariance of cohomology theories with modulus

Abstract

In this paper, we study cohomology theories of $Q$-modulus pairs, which are pairs $(X,D)$ consisting of a scheme X and a $Q$-divisor D. Our main theorem provides a sufficient condition for such a cohomology theory to be invariant under blow-ups with centers contained in the divisor. This yields a short proof of the blow-up invariance of the Hodge cohomology with modulus proved by Kelly-Miyazaki. We also define the Witt vector cohomology with modulus using the Brylinski-Kato filtration and prove its blow-up invariance.