Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHES), France. Michel Gros is a researcher at the CNRS. Takeshi Tsuji is a professor in the Graduate School of Mathematical Sciences at the University of Tokyo.

"The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts."--Gerd Faltings, Zentralblatt MATH

• *Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*Chapter IV. Cohomology of Higgs isocrystals, pg. 307*Chapter V. Almost etale coverings, pg. 449*Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599

Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHES), France. Michel Gros is a researcher at the CNRS. Takeshi Tsuji is a professor in the Graduate School of Mathematical Sciences at the University of Tokyo.

"The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts."--Gerd Faltings, Zentralblatt MATH

• *Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*Chapter IV. Cohomology of Higgs isocrystals, pg. 307*Chapter V. Almost etale coverings, pg. 449*Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599

Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHES), France. Michel Gros is a researcher at the CNRS. Takeshi Tsuji is a professor in the Graduate School of Mathematical Sciences at the University of Tokyo.

"The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts."--Gerd Faltings, Zentralblatt MATH

• *Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*Chapter IV. Cohomology of Higgs isocrystals, pg. 307*Chapter V. Almost etale coverings, pg. 449*Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599