Compact generators in categories of matrix factorizations

By Tobias Dyckerhoff. 2009

230 citations recorded by the source corpus.

We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator which is given by the stabilization of the residue field. We deduce a quasi-equivalence between the category of matrix factorizations and the dg derived category of an explicitly computable dg algebra. Building on this result, we employ a variant of Toen's derived Morita theory to identify continuous functors between matrix factorization categories as integral transforms. This enables us to calculate the Hochschild chain and cochain complexes of these categories. Finally, we give interpretations of the results of this work in terms of noncommutative geometry based on dg categories.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ac8dc1642b504c74fed301d8ba62100c9f775b14

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In Algebra and Number Theory

1. Matthew R. Ballard
2. Nick Sheridan
3. P. Seidel
4. A. Blanc
5. L. Katzarkov
6. David Favero

In Geometry and Topology

1. P. Seidel
2. L. Katzarkov
3. Nick Sheridan
4. D. Auroux
5. Matthew R. Ballard
6. David Favero
7. M. Abouzaid
8. I. Smith

Citations in the corpus

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