Noncommutative homological projective duality

TL;DR

This paper extends Kuznetsov's homological projective duality to noncommutative algebraic geometry, broadening its applicability by removing common geometric assumptions and working over general base schemes.

Contribution

It introduces a generalized framework for homological projective duality applicable to noncommutative settings and less restrictive geometric conditions.

Findings

Developed a noncommutative version of homological projective duality.

Extended the theory to work over general base schemes.

Removed smoothness, properness, and transversality assumptions.

Abstract

We generalize Kuznetsov's theory of homological projective duality to the setting of noncommutative algebraic geometry. Simultaneously, we develop the theory over general base schemes, and remove the usual smoothness, properness, and transversality hypotheses.