Motivic infinite cyclic covers
Manuel Gonzalez Villa, Anatoly Libgober, Laurentiu Maxim

TL;DR
This paper introduces a new motivic invariant called the motivic infinite cyclic cover, associated with certain infinite cyclic covers of complex manifolds, unifying various motivic Milnor fiber concepts and proving its birational invariance.
Contribution
It constructs the motivic infinite cyclic cover in the Grothendieck ring and demonstrates its birational invariance, unifying different motivic Milnor fiber notions.
Findings
Provides a new motivic invariant for infinite cyclic covers
Unifies the motivic Milnor fiber of hypersurface singularities and rational functions
Establishes birational invariance of the motivic infinite cyclic cover
Abstract
We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) an element in the Grothendieck ring , which we call {\it motivic infinite cyclic cover}, and show its birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively.
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