Motivic zeta function via dlt modification

TL;DR

This paper introduces a new motivic zeta function using dlt modifications of smooth varieties, which remains invariant under different choices of modifications, advancing the understanding of motivic invariants in algebraic geometry.

Contribution

It defines the dlt motivic zeta function for smooth varieties with regular functions, establishing its independence from the choice of dlt modification.

Findings

The dlt motivic zeta function is well-defined and invariant.

Provides a new approach to motivic invariants via dlt modifications.

Enhances the theoretical framework for motivic integration.

Abstract

Given a smooth variety $X$ and a regular function $f$ on it, by considering the dlt modification, we define the dlt motivic zeta function $Z^{\rm dlt}_{\rm mot}(s)$ which does not depend on the choice of the dlt modification.