2011/01/30 by Anatoly Preygel, Preygel, Anatoly · 1 citation
Computer Science · #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1101.5834
openalex publication_date 2011/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The derived category of a hypersurface has an action by "cohomology operations" k[t], deg t=-2, underlying the 2-periodic structure on its category of singularities (as matrix factorizations). We prove a Thom-Sebastiani type Theorem, identifying the k[t]-linear tensor products of these dg categories with coherent complexes on the zero locus of the sum potential on the product (with a support condition), and identify the dg category of colimit-preserving k[t]-linear functors between Ind-completions with Ind-coherent complexes on the zero locus of the difference potential (with a support condition). These results imply the analogous statements for the 2-periodic dg categories of matrix factorizations. Some applications include: we refine and establish the expected computation of 2-periodic Hochschild invariants of matrix factorizations; we show that the category of matrix factorizations is smooth, and is proper when the critical locus is proper; we show how Calabi-Yau structures on matrix factorizations arise from volume forms on the total space; we establish a version of Knörrer Periodicity for eliminating metabolic quadratic bundles over a base.