Matrix factorizations and singularity categories for stacks
Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2609-2642.

We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.

On étudie les factorisations matricielles d’un potentiel W qui est une section d’un fibré en droites sur un champ algébrique. On établit une relation entre la catégorie dérivée correspondante (la catégorie des D-branes de type B dans le modèle de Landau-Ginzburg avec potentiel W) et la catégorie des singularités du lieu des zéros de W généralisant un théorème d’Orlov. On utilise ce résultat pour construire des foncteurs image directe pour les factorisations matricielles à supports relativement propres.

DOI: 10.5802/aif.2788
Classification: 14A20,  14J17,  18E30
Keywords: matrix factorizations, singularity category, algebraic stack
Polishchuk, Alexander 1; Vaintrob, Arkady 1

1 Department of Mathematics, University of Oregon, Eugene, OR 97405
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Polishchuk, Alexander; Vaintrob, Arkady. Matrix factorizations and singularity categories for stacks. Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2609-2642. doi : 10.5802/aif.2788. http://archive.numdam.org/articles/10.5802/aif.2788/

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