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15 August 2011 Compact generators in categories of matrix factorizations
Tobias Dyckerhoff
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Duke Math. J. 159(2): 223-274 (15 August 2011). DOI: 10.1215/00127094-1415869

Abstract

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 differential graded (dg) derived category of an explicitly computable dg algebra. Building on this result, we employ a variant of Toën'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.

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Tobias Dyckerhoff. "Compact generators in categories of matrix factorizations." Duke Math. J. 159 (2) 223 - 274, 15 August 2011. https://doi.org/10.1215/00127094-1415869

Information

Published: 15 August 2011
First available in Project Euclid: 4 August 2011

zbMATH: 1252.18026
MathSciNet: MR2824483
Digital Object Identifier: 10.1215/00127094-1415869

Subjects:
Primary: 18E30
Secondary: 14B05

Rights: Copyright © 2011 Duke University Press

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Vol.159 • No. 2 • 15 August 2011
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