On the cohomology of reciprocity sheaves

Federico Binda, Kay Rülling, Shuji Saito

Published 2020-10-07Version 1

In this paper we show the existence of an action of Chow correspondences on the cohomology of reciprocity sheaves. In order to do so, we prove a number of structural results, such as a projective bundle formula, a blow-up formula, a Gysin sequence, and the existence of proper pushforward. In this way we recover and generalize analogous statements for the cohomology of Hodge sheaves and Hodge-Witt sheaves. Among the applications, we construct new birational invariants of smooth projective varieties and obstructions to the existence of zero-cycles of degree one from the cohomology of reciprocity sheaves.