Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Matrix factorizations in higher codimension
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 13D02, 14F05, 13D09
  • Retrieve articles in all journals with MSC (2010): 13D02, 14F05, 13D09
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