$K$-Equivalence and Integral Cohomology

Matthew Satriano; Evan Sundbo

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arXiv · 2601.22085

$K$-Equivalence and Integral Cohomology

Matthew Satriano·Evan Sundbo

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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.

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Matthew Satriano, Evan Sundbo. 2026-01-29. $K$-Equivalence and Integral Cohomology. https://arxiv.org/abs/2601.22085

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