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.
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.
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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},
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volume = {344},
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url = {https://www.numdam.org/articles/10.1016/j.crma.2007.01.023/}
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Samokhin, Alexander. On the $ \mathsf{D}$-affinity of quadrics in positive characteristic. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 377-382. doi : 10.1016/j.crma.2007.01.023. https://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.
