Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 1

Special Issue: In Honor of Eduard Looijenga, Part 2 of 3

Guest Editor: Gerard van der Geer

Motivic vanishing cycles as a motivic measure

Pages: 33 – 74

DOI: http://dx.doi.org/10.4310/PAMQ.2016.v12.n1.a2

Authors

Valery A. Lunts (Department of Mathematics, Indiana University, Bloomington, In., U.S.A.)

Olaf M. Schnürer (Mathematisches Institut, Universität Bonn, Germany)

Abstract

We show that the motivic vanishing cycles introduced by J. Denef and F. Loeser give rise to a motivic measure on the Grothendieck ring of varieties over the affine line. We discuss the relation of this motivic measure to the motivic measure we constructed earlier using categories of matrix factorizations.

Keywords

motivic vanishing cycles, motivic measure, Grothendieck ring of varieties, categorical measure, matrix factorizations, Thom–Sebastiani theorem

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