# Greenlees-May Duality in a Nutshell

## TL;DR

This paper provides a clear and well-documented proof of the Greenlees-May Duality Theorem, a significant generalization of Grothendieck's Local Duality, which has been scattered across various papers.

## Contribution

It offers the first comprehensive and accessible proof of the Greenlees-May Duality Theorem, consolidating scattered literature into a coherent exposition.

## Key findings

- Clarifies the proof of Greenlees-May Duality
- Establishes the theorem as a broad generalization of Local Duality
- Provides a useful reference for future research

## Abstract

This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and its proof is indeed a tangled web in a series of scattered papers. By carefully scrutinizing the requisite tools, we present a clear-cut well-documented proof of this theorem for the sake of bookkeeping.