Grothendieck duality made simple

TL;DR

This paper simplifies the foundations of Grothendieck duality, clarifying its distinctions from Verdier duality and making the complex theory more accessible and understandable.

Contribution

The paper provides a simplified and clearer presentation of Grothendieck duality, resolving longstanding complexities in its foundational understanding.

Findings

Simplified the conceptual framework of Grothendieck duality

Clarified the distinction between Grothendieck duality and Verdier duality

Made the foundations of coherent duality more accessible

Abstract

It has long been accepted that the foundations of Grothendieck duality are complicated. This has changed recently. By "Grothendieck duality" we mean what, in the old literature, used to go by the name "coherent duality". This isn't to be confused with what is nowadays called "Verdier duality", and used to pass as "$\ell$-adic duality".