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H 1 Local cohomology modules of a smooth $\mathbb{Z}-algebra$ have a finite number of associated primes

Auteurs : Lyubeznik, Gennady (Auteur de la Conférence)
CIRM (Editeur )

Résumé : 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.

Codes MSC :
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}

 Informations sur la Vidéo Langue : Anglais Date de publication : 25/08/14 Date de captation : 09/07/13 Collection : Research talks ; Algebra Format : quicktime ; audio/x-aac Durée : 00:56:52 Domaine : Algebra Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2013-07-09_Lyubeznik.mp4 Informations sur la rencontre Nom de la rencontre : Commutative algebra and its interactions with algebraic geometry / Algèbre commutative et ses interactions avec la géométrie algébriqueOrganisateurs de la rencontre : Bruns, Winfried ; Chardin, Marc ; Ulrich, BerndDates : 08/07/13 - 12/07/13 Année de la rencontre : 2013 Citation Data DOI : 10.24350/CIRM.V.18588503 Cite 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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