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Multi angle 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 )

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    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 rencontre

    Nom du congrès : Commutative algebra and its interactions with algebraic geometry / Algèbre commutative et ses interactions avec la géométrie algébrique
    Organisteurs Congrès : Bruns, Winfried ; Chardin, Marc ; Ulrich, Bernd
    Dates : 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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