The author defines and studies the notions of de Rham and crystalline smooth \(p\)-adic sheaves over "suitable" \(p\)-adic bases. To do this, he introduces \(p\)-adic period rings (analogous to those of J.-M. Fontaine), which are used to associate differential invariants to them. In the good reduction case, he obtains a fully faithful functor from the category of crystalline smooth \(p\)-adic sheaves in that of filtered \(F\)-isocrystals on the special fiber.

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 number theory.

Table of Contents

• Introduction
• Notations, premiéres propriétés
• L'anneau \(C\)
• Rappels sur l'anneau \(B_{HT}\) de Hyodo
• L'anneau \(B_{dR}\)
• L'anneau \(B_{cris}\)
• \((\varphi, \nabla)\)-modules filtrés
• Représentations \(p\)-adiques
• Appendices
• Bibliographie
• Index