Local cohomology based on a nonclosed support defined by a pair of ideals

Details Local cohomology based on a nonclosed support defined by a pair of ideals Local cohomology based on a nonclosed support defined by a pair of ideals

2007-09-20

arxiv.org/abs/0709.3149v2

Mathematics

Commutative Algebra

28 pages, minor corrections, to appear in J. Pure Appl. Algebra

Scientific paper

We introduce an idea for generalization of a local cohomology module, which
we call a local cohomology module with respect to a pair of ideals (I,J), and
study their various properties. Some vanishing and nonvanishing theorems are
given for this generalized version of local cohomology. We also discuss its
connection with the ordinary local cohomology.

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