Local cohomology and 𝒟-affinity in positive characteristic
[Cohomologie locale et 𝒟-affinité en caractéristique positive]
Kashiwara, Masaki1 ; Lauritzen, Niels2
1 Research Institute for Mathematical Sciences, Kyoto University, Japan
2 Institut for matematiske fag, Aarhus Universitet, Århus, Denmark
Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 993-996.

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 :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02616-X
Kashiwara, Masaki 1 ; Lauritzen, Niels 2

1 Research Institute for Mathematical Sciences, Kyoto University, Japan
2 Institut for matematiske fag, Aarhus Universitet, Århus, Denmark 
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Kashiwara, Masaki; Lauritzen, Niels. Local cohomology and $ \mathcal{D}$-affinity in positive characteristic. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 993-996. doi : 10.1016/S1631-073X(02)02616-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02616-X/

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