Six operations on dg enhancements of derived categories of sheaves

TL;DR

This paper extends the six functor formalism for derived categories of sheaves to differential graded enhancements using enriched model category theory, providing a more refined algebraic framework.

Contribution

It introduces a method to lift the six functor formalism to dg enhancements, advancing the algebraic structure of derived categories of sheaves.

Findings

Successful lifting of the six functor formalism to dg enhancements

Application of enriched model category theory in this context

Enhanced algebraic understanding of derived categories

Abstract

We lift Grothendieck-Verdier-Spaltenstein's six functor formalism for derived categories of sheaves on ringed spaces over a field to differential graded enhancements. Our main tools come from enriched model category theory.