## Matrix factorizations in higher codimension

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- by Jesse Burke and Mark E. Walker PDF
- Trans. Amer. Math. Soc.
**367**(2015), 3323-3370 Request permission

## 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.## References

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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
- Received by editor(s): November 20, 2012
- Received by editor(s) in revised form: May 2, 2013
- Published electronically: January 20, 2015
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3314810