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Local cohomology modules of a smooth $\mathbb{Z}-algebra$ have a finite number of associated primes
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Authors : Lyubeznik, Gennady (Author of the conference)
CIRM (Publisher )
13A35 - Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$, See also {13Mxx}
13D45 - Local cohomology, See also {14B15}
13F20 - Polynomial rings and ideals, See also {11C08}
13N10 - Rings of differential operators, See also {16S32, 32C38}
14B15 - Local cohomology, See also {13D45, 32C36}
CIRM (Publisher )
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Abstract :
Let $R$ be a commutative Noetherian ring that is a smooth $\mathbb{Z}-algebra$. For each ideal $a$ of $R$ and integer $k$, we prove that the local cohomology module $H^k_a(R)$ 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.
MSC Codes : 13A35 - Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$, See also {13Mxx}
13D45 - Local cohomology, See also {14B15}
13F20 - Polynomial rings and ideals, See also {11C08}
13N10 - Rings of differential operators, See also {16S32, 32C38}
14B15 - Local cohomology, See also {13D45, 32C36}
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 25/08/14 Conference Date : 09/07/13 Subseries : Research talks arXiv category : Commutative Algebra Mathematical Area(s) : Algebra Format : MP4 (.mp4) - HD Video Time : 00:56:52 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2013-07-09_Lyubeznik.mp4 
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Information on the Event
Event Title : Commutative algebra and its interactions with algebraic geometry / Algèbre commutative et ses interactions avec la géométrie algébriqueEvent Organizers : Bruns, Winfried ; Chardin, Marc ; Ulrich, Bernd Dates : 08/07/13 - 12/07/13 Event Year : 2013
Citation Data
DOI : 10.24350/CIRM.V.18588503Cite this video as: Lyubeznik, Gennady (2013). Local cohomology modules of a smooth $\mathbb{Z}-algebra$ have a finite number of associated primes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18588503 URI : http://dx.doi.org/10.24350/CIRM.V.18588503 |
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