$K$-Equivalence and Integral Cohomology

Matthew Satriano; Evan Sundbo

doi:10.48550/arxiv.2601.22085

$K$-Equivalence and Integral Cohomology

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Matthew Satriano, Evan Sundbo

DOI: 10.48550/arxiv.2601.22085

Cited by: 0

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.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Homotopy and Cohomology in Algebraic Topology Advanced Algebra and Geometry

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 29 January 2026
Document type: Preprint