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Journal of Noncommutative Geometry

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Volume 10, Issue 3, 2016, pp. 981–1042
DOI: 10.4171/JNCG/253

Published online: 2016-09-28

Matrix factorizations and motivic measures

Valery A. Lunts[1] and Olaf M. Schnürer[2]

(1) Indiana University, Bloomington, USA
(2) Universität Bonn, Germany

This article is the continuation of [17]. We use categories of matrix factorizations to define a morphism of rings (= a Landau–Ginzburg motivic measure) from the (motivic) Grothendieck ring of varieties over $\mathbb A^1$ to the Grothendieck ring of saturated dg categories (with relations coming from semi-orthogonal decompositions into admissible subcategories). Our Landau–Ginzburg motivic measure is the analog for matrix factorizations of the motivic measure in [5] whose definition involved bounded derived categories of coherent sheaves. On the way we prove smoothness and a Thom–Sebastiani theorem for enhancements of categories of matrix factorizations.

Keywords: Matrix factorization, motivic measure, Grothendieck ring of saturated dg categories, smoothness, Thom–Sebastiani theorem

Lunts Valery, Schnürer Olaf: Matrix factorizations and motivic measures. J. Noncommut. Geom. 10 (2016), 981-1042. doi: 10.4171/JNCG/253