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Matrix factorizations in higher codimension


Authors: Jesse Burke and Mark E. Walker
Journal: Trans. Amer. Math. Soc. 367 (2015), 3323-3370
MSC (2010): Primary 13D02, 14F05, 13D09
DOI: https://doi.org/10.1090/S0002-9947-2015-06323-5
Published electronically: January 20, 2015
MathSciNet review: 3314810
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Abstract: We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this equivalence, we give a geometric construction of the ring of cohomology operators, and a generalization of the theory of support varieties, which we call stable support sets. We settle a question of Avramov about which stable support sets can arise for a given complete intersection ring. We also use the equivalence to construct a projective resolution of a module over a complete intersection ring from a matrix factorization, generalizing the well-known result in the hypersurface case.


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Additional Information

Jesse Burke
Affiliation: Department of Mathematics, Universität Bielefeld, 33501 Bielefeld, Germany
Email: jburke@math.uni-bielefeld.de

Mark E. Walker
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Email: mwalker5@math.unl.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06323-5
Received by editor(s): November 20, 2012
Received by editor(s) in revised form: May 2, 2013
Published electronically: January 20, 2015
Article copyright: © Copyright 2015 American Mathematical Society