Matrix factorizations and singularity categories for stacks
Annales de l'Institut Fourier, Volume 61 (2011) no. 7, p. 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 : https://doi.org/10.5802/aif.2788
Classification:  14A20,  14J17,  18E30
Keywords: matrix factorizations, singularity category, algebraic stack
@article{AIF_2011__61_7_2609_0,
     author = {Polishchuk, Alexander and Vaintrob, Arkady},
     title = {Matrix factorizations and singularity categories for stacks},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {7},
     year = {2011},
     pages = {2609-2642},
     doi = {10.5802/aif.2788},
     mrnumber = {3112502},
     zbl = {1278.13014},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_7_2609_0}
}
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://www.numdam.org/item/AIF_2011__61_7_2609_0/

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