Duality and symmetry of complexity over complete intersections via exterior homology

Liu, Jian; Pollitz, Josh

doi:10.1090/proc/15276

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

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.

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