Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 14 (2019), 17 -- 48

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This work is licensed under a Creative Commons Attribution 4.0 International License.


Hossein Faridian

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.

2010 Mathematics Subject Classification: 16L30; 16D40; 13C05.
Keywords: ℑomplex; derived category; Greenlees-May duality; Koszul complex; local cohomology; local homology.

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Hossein Faridian,
School of Mathematical and Statistical Sciences,
Clemson University, SC 29634, USA.