$K$-Equivalence and Integral Cohomology

Abstract

We introduce an integral version of the Hodge polynomial, which encodes the integral cohomology of smooth projective varieties. We prove it extends to a function which is well-defined on the Grothendieck ring of varieties and we obtain as a consequence that $K$-equivalent smooth projective varieties have isomorphic integral cohomology groups.

arXiv comment7 pages, comments are welcome! This version includes references to work in which the main result was previously shown to be true, which we were made aware of after the first version was posted