Duality and symmetry of complexity over complete intersections via exterior homology

TL;DR

This paper explores the homological properties of locally complete intersection rings using exterior algebra, demonstrating self-duality of certain subcategories and symmetry of complexity.

Contribution

It provides new proofs of self-duality of thick subcategories and symmetry of complexity for complete intersections, extending previous results to a broader setting.

Findings

Thick subcategories are self-dual under Grothendieck duality.

Complete intersections exhibit symmetry of complexity.

Two independent proofs are provided for these properties.

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.