Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants
Name
809687451-MIT.pdf
Description
Full printable version
Size
8.78 MB
Format
Adobe PDF
Checksum (MD5)
7dcac18d684fd7cfd85d8d4d12ae3b77
Author(s)
Preygel, Anatoly
Advisor(s)
Jacob A. Lurie.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
Abstract
The derived category of a hypersurface has an action by "cohomology operations" k[[beta]], deg[beta] = 2, underlying the 2-periodic structure on its category of singularities (as matrix factorizations). We prove a Thom-Sebastiani type Theorem, identifying the k[[beta]]-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[[beta]]-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. We also present a viewpoint on matrix factorizations in terms of (formal) groups actions on categories that is conducive to formulating functorial statements and in particular to the computation of higher algebraic structures on Hochschild invariants. 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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 149-150).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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