2013/10/28 by Valery A. Lunts, Lunts, Valery A., Olaf M. Schnürer +1
Mathematics · #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.CT #math.RT
paper · pdf · doi:10.48550/arxiv.1310.7640
51 pages, minor improvements
arxiv created 2015/06/01 · arxiv updated 2015/06/02
This article is the continuation of [LS12]. 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 \mathbbA1 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 [BLL04] 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.