A local homology theory for linearly compact modules

Details A local homology theory for linearly compact modules A local homology theory for linearly compact modules

2007-09-12

arxiv.org/abs/0709.1778v1

Mathematics

Commutative Algebra

24 pages

Scientific paper

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local homology modules of linearly compact modules are proved. A duality theory between local homology and local cohomology modules of linearly compact modules is developed by using Matlis duality and Macdonald duality. As consequences of the duality theorem we obtain some generalizations of well-known results in the theory of local cohomology for semi-discrete linearly compact modules.

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