Local cohomology and Gorenstein injective dimension over local homomorphisms

Details Local cohomology and Gorenstein injective dimension over local homomorphisms Local cohomology and Gorenstein injective dimension over local homomorphisms

2006-05-22

arxiv.org/abs/math/0605580v1

Mathematics

Commutative Algebra

Scientific paper

A generalization of Grothendieck's non-vanishing theorem is proved for a
module which is finite over a local homomorphism. It is also proved that the
Gorenstein injective dimension of such a module, if finite, is bounded below by
its Krull dimension and is equal to the supremum of the depths of the
localizations of the ring over primes in the support of the module.

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