Finitely graded local cohomology and the depths of graded algebras

Author:
Thomas Marley

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3601-3607

MSC:
Primary 13A30; Secondary 13C15, 13D45

MathSciNet review:
1283558

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Abstract | References | Similar Articles | Additional Information

Abstract: The term "finitely graded" is introduced here to refer to graded modules which are nonzero in only finitely many graded pieces. We consider the question of when the local cohomology modules of a graded module are finitely graded. Using a theorem of Faltings concerning the annihilation of local cohomology, we obtain some partial answers to this question. These results are then used to compare the depths of the Rees algebra and the associated graded ring of an ideal in a local ring.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1283558-0

Keywords:
Local cohomology,
Rees algebra,
associated graded ring

Article copyright:
© Copyright 1995
American Mathematical Society