Local cohomology and $ \mathcal{D}$-affinity in positive characteristic

Masaki Kashiwara; Niels Lauritzen

doi:10.1016/S1631-073X(02)02616-X

Local cohomology and

𝒟

-affinity in positive characteristic
[Cohomologie locale et

𝒟

-affinité en caractéristique positive]

Masaki Kashiwara ¹ ; Niels Lauritzen ²

¹ Research Institute for Mathematical Sciences, Kyoto University, Japan
² Institut for matematiske fag, Aarhus Universitet, Århus, Denmark

Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 993-996.

Résumé
Abstract

On donne un exemple d'un $𝒟$ -module sur une variété grassmannienne en caractéristique positive avec premier groupe de cohomologie non nul. On obtient ainsi un contre-exemple à la $𝒟$ -affinité et à équivalence de Beilinson–Bernstein pour les variétés des drapeaux en caractéristique positive.

We give an example of a $𝒟$ -module on a Grassmann variety in positive characteristic with non-vanishing first cohomology group. This is a counterexample to $𝒟$ -affinity and the Beilinson–Bernstein equivalence for flag manifolds in positive characteristic.

Reçu le : 2002-10-14
Accepté le : 2002-10-23
Publié le : 2002-11-21

DOI : 10.1016/S1631-073X(02)02616-X

Affiliations des auteurs :

Masaki Kashiwara ¹ ; Niels Lauritzen ²

¹ Research Institute for Mathematical Sciences, Kyoto University, Japan
² Institut for matematiske fag, Aarhus Universitet, Århus, Denmark

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     author = {Masaki Kashiwara and Niels Lauritzen},
     title = {Local cohomology and $ \mathcal{D}$-affinity in positive characteristic},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {993--996},
     publisher = {Elsevier},
     volume = {335},
     number = {12},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02616-X},
     language = {en},
}

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Masaki Kashiwara; Niels Lauritzen. Local cohomology and $ \mathcal{D}$-affinity in positive characteristic. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 993-996. doi : 10.1016/S1631-073X(02)02616-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02616-X/

Bibliographie
Cité par

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[2] R. Bezrukavnikov, I. Mirković, D. Rumynin, Localization of modules for a semisimple Lie algebra in prime characteristic, Preprint, | arXiv

[3] C. Peskine; L. Szpiro Dimension projective finie et cohomologie locale, Inst. Hautes Études Sci. Publ. Math., Volume 42 (1973), pp. 47-119

[4] B. Haastert Über Differentialoperatoren und $𝒟$ -Moduln in positiver Characteristik, Manuscripta Math., Volume 58 (1987), pp. 385-415

[5] C. Huneke; G. Lyubeznik On the vanishing of local cohomology modules, Invent. Math., Volume 102 (1990), pp. 73-95

[6] G. Kempf The Grothendieck–Cousin complex of an induced representation, Adv. Math., Volume 29 (1978), pp. 310-396

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