On the cohomology of reciprocity sheaves
Abstract
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 blowup 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 HodgeWitt sheaves. We give several applications of the general theory to problems which have been classically studied. Among these applications, we construct new birational invariants of smooth projective varieties and obstructions to the existence of zerocycles of degree one from the cohomology of reciprocity sheaves.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.03301
 Bibcode:
 2020arXiv201003301B
 Keywords:

 Mathematics  Algebraic Geometry;
 14F43;
 14F05;
 14C25
 EPrint:
 111 pages. Final version, to appear in Forum of Math. Sigma