Journal of Noncommutative Geometry
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Published online: 2016-09-28
Matrix factorizations and motivic measuresValery A. Lunts and Olaf M. Schnürer (1) Indiana University, Bloomington, USA
(2) Universität Bonn, Germany
This article is the continuation of . 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  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