Rationalite des series de Poincare et des fonctions Zeta motiviques

TL;DR

This paper proves that for certain algebraic varieties over fields of characteristic zero, the associated motivic Poincare series and Zeta functions are rational functions.

Contribution

It establishes the rationality of motivic Poincare series and Zeta functions for flat, purely dimensional varieties over characteristic zero fields.

Findings

Motivic Poincare series are rational for the considered varieties.

Motivic Zeta functions are rational in this setting.

Results extend understanding of motivic invariants in algebraic geometry.

Abstract

If k is a field of characteristic 0, we prove that the motivic Poincare serie and the motivic Zeta functions associated to a k[[t]]-variety, flat and purely dimensional, are rational.