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.
Keywords: matrix factorizations, singularity category, algebraic stack
Mot clés : factorisations matricielles, catégorie des singularités, champ algébrique
@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}, pages = {2609--2642}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {7}, year = {2011}, doi = {10.5802/aif.2788}, zbl = {1278.13014}, mrnumber = {3112502}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2788/} }
TY - JOUR AU - Polishchuk, Alexander AU - Vaintrob, Arkady TI - Matrix factorizations and singularity categories for stacks JO - Annales de l'Institut Fourier PY - 2011 SP - 2609 EP - 2642 VL - 61 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2788/ DO - 10.5802/aif.2788 LA - en ID - AIF_2011__61_7_2609_0 ER -
%0 Journal Article %A Polishchuk, Alexander %A Vaintrob, Arkady %T Matrix factorizations and singularity categories for stacks %J Annales de l'Institut Fourier %D 2011 %P 2609-2642 %V 61 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2788/ %R 10.5802/aif.2788 %G en %F 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/articles/10.5802/aif.2788/
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