A construction of tame sheaves and tame de Rham--Witt cohomology

Abstract

In this article, we consider an algebraic version of the tame site of a pair $(X,\widetilde{X})$. With this definition, we provide a general machinery to construct a tame sheaf from the data of an étale sheaf on $X$ and a family of local tame sections. We apply this construction to the big de Rham--Witt sheaves with tame sections defined by log poles and, over a field, to reciprocity sheaves, and deduce some consequences. As an application, we compare tame syntomic cohomology with the Nygaard filtration on the tame de Rham--Witt complex.