Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Duality and symmetry of complexity over complete intersections via exterior homology


Authors: Jian Liu and Josh Pollitz
Journal: Proc. Amer. Math. Soc. 149 (2021), 619-631
MSC (2020): Primary 13D09; Secondary 13D07, 13H10, 16E45
DOI: https://doi.org/10.1090/proc/15276
Published electronically: December 16, 2020
MathSciNet review: 4198070
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 13D09, 13D07, 13H10, 16E45

Retrieve articles in all journals with MSC (2020): 13D09, 13D07, 13H10, 16E45


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: liuj231@mail.ustc.edu.cn

Josh Pollitz
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
MR Author ID: 1335525
Email: pollitz@math.utah.edu

Keywords: Complete intersections, thick subcategories, exterior algebra, Koszul complex, DG algebra, DG module, support variety, duality, complexity
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
Article copyright: © Copyright 2020 American Mathematical Society