Greenlees-May duality in a nutshell

Abstract

This expository article delves deep into Greenlees-May Duality which is widely thought of as a far-reaching generalization of Grothendieck's Local Duality. Despite its focal role in the theory of derive local homology and cohomology, in the literature this theorem did not get the treatment it deserves, as indeed its proof is 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 reference.

Keywords

• ℑomplex
• derived category
• Greenlees-May duality
• Koszul complex
• local cohomology