Matrix factorizations in higher codimension
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 wellknown result in the hypersurface case.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 DOI:
 10.48550/arXiv.1205.2552
 arXiv:
 arXiv:1205.2552
 Bibcode:
 2012arXiv1205.2552B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry
 EPrint:
 41 pages