Matrix factorizations and motivic measures
Valery A. Lunts
Indiana University, Bloomington, USAOlaf M. Schnürer
Universität Bonn, Germany
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Abstract
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 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.
Cite this article
Valery A. Lunts, Olaf M. Schnürer, Matrix factorizations and motivic measures. J. Noncommut. Geom. 10 (2016), no. 3, pp. 981–1042
DOI 10.4171/JNCG/253