Linear Koszul Duality

TL;DR

This paper develops a new form of Koszul duality relating derived categories of equivariant sheaves on derived intersections of subbundles and their orthogonals, with potential applications to Hecke algebras.

Contribution

It introduces a novel Koszul duality equivalence for derived intersections of subbundles and their orthogonals within vector bundles.

Findings

Establishes a duality equivalence between derived categories of sheaves on derived intersections.

Provides a framework for applications to Hecke algebras.

Advances understanding of derived intersection theory in algebraic geometry.

Abstract

In this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a "Koszul duality" equivalence between derived categories of G_m-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the corresponding derived intersection of the orthogonals of F_1 and F_2 inside the dual vector bundle E^*. We also propose applications to Hecke algebras.