The Bornological Dual of the Structure Sheaves of Complex Manifolds

TL;DR

This paper provides an alternative proof of bornological Verdier duality for complex manifolds, utilizing quasi-abelian homological algebra and residue theory to deepen understanding of duality in complex geometry.

Contribution

It introduces a new proof approach for bornological Verdier duality, expanding the theoretical framework with quasi-abelian homological algebra and residue theory.

Findings

Alternative proof of bornological Verdier duality

Application of Schneider's quasi-abelian homological algebra

Enhanced understanding of duality in complex manifolds

Abstract

An alternative proof of bornological Verdier duality for complex manifolds, as proven initially by Prosmans & Schneiders is given, using Schneider's theory of quasi-abelian homological algebra, and the theory of residues and duality.