On the $ \mathsf{D}$-affinity of quadrics in positive characteristic

Alexander Samokhin

doi:10.1016/j.crma.2007.01.023

Algebraic Geometry

On the

D

-affinity of quadrics in positive characteristic

Presented by: Michel Raynaud

Alexander Samokhin ¹

¹ Institute for Information Transmission Problems, B. Karetnyj per., 19, 127994, Moscow, Russia

Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 377-382.

Abstract
Résumé

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 $D$ -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 $D$ -affines. Enfin, nous discutons des applications de ce résultat à des catégories dérivées des faisceaux cohérents.

Received: 2005-12-30
Accepted: 2007-01-06
Published online: 2007-03-09

DOI: 10.1016/j.crma.2007.01.023

Author's affiliations:

Alexander Samokhin ¹

¹ Institute for Information Transmission Problems, B. Karetnyj per., 19, 127994, Moscow, Russia

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     title = {On the $ \mathsf{D}$-affinity of quadrics in positive characteristic},
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     pages = {377--382},
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Alexander Samokhin. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.023/

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Cited by Sources:

^⁎ This work was supported in part by a French Government Fellowship and by the RFBR grant No. 02-01-22005.

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