Motivic measures and stable birational geometry

TL;DR

This paper explores the motivic Grothendieck group in stable birational geometry, providing a counter-example to Kapranov's conjecture on motivic zeta-function rationality.

Contribution

It introduces a new perspective on motivic measures and presents a counter-example challenging a prior conjecture in the field.

Findings

Counter-example to Kapranov's conjecture on motivic zeta-function rationality

Insights into the structure of the motivic Grothendieck group

Advances understanding of stable birational invariants

Abstract

We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.