Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2012
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| Online Access: | http://hdl.handle.net/1721.1/73373 |
| _version_ | 1826196136692547584 |
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| author | Preygel, Anatoly |
| author2 | Jacob A. Lurie. |
| author_facet | Jacob A. Lurie. Preygel, Anatoly |
| author_sort | Preygel, Anatoly |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T10:22:03Z |
| format | Thesis |
| id | mit-1721.1/73373 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:22:03Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/733732019-04-12T09:20:19Z Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants Preygel, Anatoly Jacob A. Lurie. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 149-150). 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. by Anatoly Preygel. Ph.D. 2012-09-27T15:26:34Z 2012-09-27T15:26:34Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73373 809687451 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 150 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Preygel, Anatoly Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title | Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title_full | Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title_fullStr | Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title_full_unstemmed | Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title_short | Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants |
| title_sort | thom sebastiani and duality for matrix factorizations and results on the higher structures of the hochschild invariants |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73373 |
| work_keys_str_mv | AT preygelanatoly thomsebastianianddualityformatrixfactorizationsandresultsonthehigherstructuresofthehochschildinvariants |