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Lectures on local cohomology and duality. (English) Zbl 1011.13010
Lyubeznik, Gennady (ed.), Local cohomology and its applications. Selected papers of the international workshop, Guanajuato, Mexico. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 226, 39-89 (2002).
This is a brief textbook on the local duality theorem. The author reviews derived categories and functors in a new point of view and gives some new proofs and generalizations of known theorems. For example, he defines right and left derived functors on unbounded complexes. Furthermore, he explains the Greenless-May duality, which is an analogue of the local duality theorem for non-local rings.
For the entire collection see [Zbl 0974.00036].

13D45 Local cohomology and commutative rings
13D25 Complexes (MSC2000)
14B15 Local cohomology and algebraic geometry
18E25 Derived functors and satellites (MSC2010)