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

Mathematics

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

21 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

Funding Information:
B.B. was supported by NSF grants DMS 1160914 and DMS 1128155, M.B. by DFG grants SFB/TRR45 and his Heisenberg Professorship, G.L. by NSF grant DMS 1161783, A.K.S. by NSF grant DMS 1162585, and W.Z. by NSF grant DMS 1068946. A.K.S. thanks Uli Walther for several valuable discussions. The authors are grateful to the American Institute of Mathematics (AIM) for supporting their collaboration. All authors were also supported by NSF grant 0932078000 while in residence at MSRI.

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

Keywords

13A35
13D45
13F20
13N10
14B15

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AU - Blickle, Manuel

AU - Lyubeznik, Gennady

AU - Singh, Anurag K.

AU - Zhang, Wenliang

N1 - Funding Information: B.B. was supported by NSF grants DMS 1160914 and DMS 1128155, M.B. by DFG grants SFB/TRR45 and his Heisenberg Professorship, G.L. by NSF grant DMS 1161783, A.K.S. by NSF grant DMS 1162585, and W.Z. by NSF grant DMS 1068946. A.K.S. thanks Uli Walther for several valuable discussions. The authors are grateful to the American Institute of Mathematics (AIM) for supporting their collaboration. All authors were also supported by NSF grant 0932078000 while in residence at MSRI. Publisher Copyright: © 2013, Springer-Verlag Berlin Heidelberg.

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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.

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

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