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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Duality and symmetry of complexity over complete intersections via exterior homology
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by Jian Liu and Josh Pollitz PDF
Proc. Amer. Math. Soc. 149 (2021), 619-631 Request permission


We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally complete intersection ring are self-dual under Grothendieck duality. This was proved by Stevenson when the ring is a quotient of a regular ring modulo a regular sequence; we offer two independent proofs in the more general setting. Second, we use these techniques to supply new proofs that complete intersections possess symmetry of complexity.
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Additional Information
  • Jian Liu
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
  • ORCID: 0000-0001-8360-7024
  • Email:
  • Josh Pollitz
  • Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
  • MR Author ID: 1335525
  • Email:
  • Received by editor(s): June 15, 2020
  • Received by editor(s) in revised form: July 11, 2020
  • Published electronically: December 16, 2020
  • Additional Notes: The first author thanks the China Scholarship Council for financial support to visit Srikanth Iyengar at the University of Utah.
    The second author was supported by the National Science Foundation under Grant No. 1840190.
  • Communicated by: Sarah Witherspoon
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 619-631
  • MSC (2020): Primary 13D09; Secondary 13D07, 13H10, 16E45
  • DOI:
  • MathSciNet review: 4198070