Représentations p-adiques cristallines de de Rham dans le cas relatif
In this booklet, the author develops a theory of the Fontaine functors Dcris and DdR for smooth p-adic sheaves over a suitable affine p-adic base. The bulk of this work consists of a detailed study of various period rings (BHT, Bcris and BdR) in this setting. The main result states that - in the good reduction case - the functor Dcris is fully faithful. Its essential image is described only for one-dimensional crystalline representations.