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La geometrie rigide est devenue, au fil des ans, un outil indispensable dans un grand nombre de questions en geometrie arithmetique. Depuis ses premieres fondations, posees par J. Tate en 1961, la theorie s'est developpee dans des directions variees. Ce livre est le premier volume d'un traite qui expose un developpement systematique de la geometrie rigide suivant l'approche de M. Raynaud, basee sur les schemas formels a eclatements admissibles pres. Ce volume est consacre a la construction des espaces rigides dans une situation relative et a l'etude de leurs proprietes geometriques....

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.

The first approach relies on a...

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.

The first approach relies on a...