Linear Koszul Duality II - Coherent sheaves on perfect sheaves

TL;DR

This paper extends the theory of linear Koszul duality, a geometric duality relating modules over symmetric and exterior algebras, by constructing it in a broad setting and establishing its compatibility with morphisms and base change.

Contribution

It develops a general construction of linear Koszul duality and proves its compatibility with morphisms of vector bundles and base change, advancing the geometric understanding of the duality.

Findings

Constructed linear Koszul duality in a very general setting.

Proved compatibility with morphisms of vector bundles.

Established base change compatibility for the duality.

Abstract

In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change.