In the first half of the book, the author translates in the geometric situation of Drinfeld varieties, that is, the case of a function field of one variable over a finite field, the principal results of the book of Michael Harris and Richard Taylor, which treats some Shimura varieties over number fields. The author gives in particular the restriction of sheaves to the open strata of vanishing cycles in terms of some local systems, known as Harris-Taylor's local systems, for which he calculates the alternating sum of the cohomology group with compact supports. In the last half of the book, the author describes the monodromy filtration of the perverse sheaf of vanishing cycles and the spectral sequence associated to it. Thanks to the Berkovich-Fargues theorem, the author obtains the description of the local monodromy filtration of the Deligne-Carayol model.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

• Variétés d'Igusa, systèmes locaux de Harris-Taylor et cycles évanescents des variétés de Drinfeld
• Groupes de cohomologie du modèle local: cas Iwahori
• Description de la somme alternée des groupes de cohomologie
• Filtration de monodromie des cycles évanescents
• Compléments sur la cohomologie globale et applications
• Figures
• Bibliography