Fibre de Milnor motivique a l'infini

TL;DR

This paper introduces a motivic Milnor fiber at infinity for regular maps from smooth complex varieties to the affine line, and computes it explicitly for non-degenerate Laurent polynomials using Newton polyhedra at infinity.

Contribution

It defines a new concept of motivic Milnor fiber at infinity and provides explicit computations for a class of Laurent polynomials, extending the understanding of motivic invariants at infinity.

Findings

Motivic Milnor fiber at infinity is well-defined for certain regular maps.

Explicit computation for non-degenerate Laurent polynomials.

Connection between Newton polyhedra at infinity and motivic invariants.

Abstract

Given a regular map f from a smooth complex variety to the affine line, we define a motivic Milnor fiber at infinity and we compute it in the case of a non degenerate Laurent polynomial for its Newton polyhedra at infinity.