The derived category of the abelian category of constructible sheaves

TL;DR

This paper proves an equivalence between the triangulated category of constructible complexes and the derived category of constructible sheaves on an algebraic variety, extending Nori's theorem to positive characteristic.

Contribution

It generalizes Nori's theorem by establishing the equivalence in positive characteristic, linking constructible complexes with derived categories of constructible sheaves.

Findings

Equivalence of categories established in positive characteristic.

Extension of Nori's theorem to broader setting.

Provides foundational link between constructible complexes and sheaves.

Abstract

We show that the triangulated category of bounded constructible complexes on an algebraic variety X over an algebraically closed field is equivalent to the bounded derived category of the abelian category of constructible sheaves on X, extending a theorem of Nori to the case of positive characteristic.