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Proregular sequences, local cohomology, and completion. (English) Zbl 1023.13011
This is an improvement of a paper by J. P. C. Greenlees and J. P. May [J. Algebra 149, No. 2, 438-453 (1992, Zbl 0774.18007)]. Local homology is a dual notion of local cohomology. There are two different definition of it: the homology of co-Čech complex and the left derived functor of completion. J. P. C. Greenlees and J. P. May gave a sufficient condition (loc. cit.) that they coincide. In the present article, the author gives a necessary and sufficient condition that the two definitions of local homology coincide.

13D45 Local cohomology and commutative rings
14B15 Local cohomology and algebraic geometry
13D25 Complexes (MSC2000)
local homology
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