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

22 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

Bibliographical note

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

Keywords

13A35
13D45
13F20
13N10
14B15

Publisher link

10.1007/s00222-013-0490-z

Find It

Find It at U of M Libraries

Cite this

@article{003417bde2ce4cf8bb610a362383fcc0,

title = "Local cohomology modules of a smooth Z-algebra have finitely many associated primes",

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.",

keywords = "13A35, 13D45, 13F20, 13N10, 14B15",

author = "Bhargav Bhatt and Manuel Blickle and Gennady Lyubeznik and Singh, {Anurag K.} and Wenliang Zhang",

note = "Publisher Copyright: {\textcopyright} 2013, Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = sep,

day = "1",

doi = "10.1007/s00222-013-0490-z",

language = "English (US)",

volume = "197",

pages = "509--519",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=84956829026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956829026&partnerID=8YFLogxK

U2 - 10.1007/s00222-013-0490-z

DO - 10.1007/s00222-013-0490-z

M3 - Article

AN - SCOPUS:84956829026

SN - 0020-9910

VL - 197

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

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this