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Crystalline and de Rham p-adic representations in the relative case) We define and study the notions of de Rham and crystalline smooth p-adic sheaves over "suitable" p-adic bases. To do this, we introduce 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, we obtain a fully faithful functor from the category of crystalline smooth p-adic sheaves in that of filtred F -isocrystals on the special fiber. c © Mémoires de la Société Mathématique de France 112, SMF 2008

Représentations p-adiques cristallines et de de Rham dans le cas relatif