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Let X_d be the p-adic analytic space classifying the d-dimensional(semisimple) p-adic Galois representations of the absolute Galois group of Q_p.We show that the crystalline representations are Zarski-dense in manyirreducible components of X_d, including the components made of residuallyirreducible representations. This extends to any dimension d previous resultsof Colmez and Kisin for d = 2. For this we construct an analogue of theinfinite fern of Gouv\^ea-Mazur in this context, based on a study of analyticfamilies of trianguline (phi,Gamma)-modules over the Robba ring. We show inparticular the existence of a universal family of (framed, regular) trianguline(phi,Gamma)-modules, as well as the density of the crystalline(phi,Gamma)-modules in this family. These results may be viewed as a localanalogue of the theory of p-adic families of finite slope automorphic forms,they are new already in dimension 2. The technical heart of the paper is acollection of results about the Fontaine-Herr cohomology of families oftrianguline (phi,Gamma)-modules.

Sur la densit\'e des repr\'esentations cristallines du groupe de Galois absolu de Q_p