no. 12
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 
@article{CRMATH_2002__335_12_993_0,
     author = {Kashiwara, Masaki and Lauritzen, Niels},
     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},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02616-X/}
}
TY  - JOUR
AU  - Kashiwara, Masaki
AU  - Lauritzen, Niels
TI  - Local cohomology and $ \mathcal{D}$-affinity in positive characteristic
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 993
EP  - 996
VL  - 335
IS  - 12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02616-X/
DO  - 10.1016/S1631-073X(02)02616-X
LA  - en
ID  - CRMATH_2002__335_12_993_0
ER  - 
%0 Journal Article
%A Kashiwara, Masaki
%A Lauritzen, Niels
%T Local cohomology and $ \mathcal{D}$-affinity in positive characteristic
%J Comptes Rendus. Mathématique
%D 2002
%P 993-996
%V 335
%N 12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02616-X/
%R 10.1016/S1631-073X(02)02616-X
%G en
%F CRMATH_2002__335_12_993_0
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/

[1] Beilinson, A.; Bernstein, J. Localisation de 𝔤-modules, C. R. Acad. Sci. Paris, Volume 292 (1981), pp. 15-18

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

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

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

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

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

Cité par Sources :