Local cohomology modules of a smooth Z-algebra have finitely many associated primes

Bhargav Bhatt; Manuel Blickle; Gennady Lyubeznik; Anurag K. Singh; Wenliang Zhang

doi:10.1007/s00222-013-0490-z

Local cohomology modules of a smooth Z-algebra have finitely many associated primes

Bhargav Bhatt
, Manuel Blickle
, Gennady Lyubeznik
, Anurag K. Singh
, Wenliang Zhang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

Let R be a commutative Noetherian ring that is a smooth Z-algebra. For each ideal a of R and integer k, we prove that the local cohomology module (Formula presented.) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.

Original language	English (US)
Pages (from-to)	509-519
Number of pages	11
Journal	Inventiones Mathematicae
Volume	197
Issue number	3
DOIs	https://doi.org/10.1007/s00222-013-0490-z
State	Published - Sep 1 2014

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Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.

Keywords

13A35
13D45
13F20
13N10
14B15

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10.1007/s00222-013-0490-z

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abstract = "Let R be a commutative Noetherian ring that is a smooth Z-algebra. For each ideal a of R and integer k, we prove that the local cohomology module (Formula presented.) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.",

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T1 - Local cohomology modules of a smooth Z-algebra have finitely many associated primes

AU - Bhatt, Bhargav

AU - Blickle, Manuel

AU - Lyubeznik, Gennady

AU - Singh, Anurag K.

AU - Zhang, Wenliang

PY - 2014/9/1

Y1 - 2014/9/1

N2 - Let R be a commutative Noetherian ring that is a smooth Z-algebra. For each ideal a of R and integer k, we prove that the local cohomology module (Formula presented.) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.

AB - Let R be a commutative Noetherian ring that is a smooth Z-algebra. For each ideal a of R and integer k, we prove that the local cohomology module (Formula presented.) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.

KW - 13A35

KW - 13D45

KW - 13F20

KW - 13N10

KW - 14B15

UR - https://www.scopus.com/pages/publications/84956829026

UR - https://www.scopus.com/pages/publications/84956829026#tab=citedBy

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DO - 10.1007/s00222-013-0490-z

M3 - Article

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SP - 509

EP - 519

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 3

ER -

Local cohomology modules of a smooth Z-algebra have finitely many associated primes

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