[Sur la -affinité de quadriques en caractéristique positive]
Dans cette Note nous étudions les anneaux des opérateurs différentiels sur les quadriques en petite dimension en caractéristique positive. Nous démontrons un théorème d'annulation pour le premier terme de la p-filtration sur les anneaux des opérateurs différentiels sur ces quadriques. Une telle annulation est une condition nécessaire pour que ces variétés soient -affines. Enfin, nous discutons des applications de ce résultat à des catégories dérivées des faisceaux cohérents.
In this Note we deal with the rings of differential operators on quadrics of low dimension in positive characteristic. We prove a vanishing theorem for the first term of the p-filtration on the rings of differential operators on such quadrics. Such a vanishing is a necessary condition for the -affinity of these varieties. We also discuss applications of this result to derived categories of coherent sheaves.
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@article{CRMATH_2007__344_6_377_0,
author = {Samokhin, Alexander},
title = {On the $ \mathsf{D}$-affinity of quadrics in positive characteristic},
journal = {Comptes Rendus. Math\'ematique},
pages = {377--382},
publisher = {Elsevier},
volume = {344},
number = {6},
year = {2007},
doi = {10.1016/j.crma.2007.01.023},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.023/}
}
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AU - Samokhin, Alexander
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JO - Comptes Rendus. Mathématique
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EP - 382
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Samokhin, Alexander. On the $ \mathsf{D}$-affinity of quadrics in positive characteristic. Comptes Rendus. Mathématique, Tome 344 (2007) no. 6, pp. 377-382. doi : 10.1016/j.crma.2007.01.023. http://www.numdam.org/articles/10.1016/j.crma.2007.01.023/
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⁎ This work was supported in part by a French Government Fellowship and by the RFBR grant No. 02-01-22005.
