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The p-adic Simpson Correspondence (AM-193)
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The p-adic Simpson Correspondence (AM-193)

Ahmed Abbes, Michel Gros, and Takeshi Tsuji

Abstract

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. It mainly focuses on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thick ... More

Keywords: p-adic Simpson correspondence, Gerd Faltings, p-adic field, linear algebra, Higgs bundle, period ring, crystalline-type topos, Higgs isocrystal, p-adic Hodge theory

Bibliographic Information

Print publication date: 2016 Print ISBN-13: 9780691170282
Published to University Press Scholarship Online: October 2017 DOI:10.23943/princeton/9780691170282.001.0001

Authors

Affiliations are at time of print publication.

Ahmed Abbes, author
French National Center for Scientific Research (CNRS)/Institute of Advanced Scientific Studies (IHÉS)

Michel Gros, author
Institut de Recherche Mathématiques de Rennes

Takeshi Tsuji, author
University of Tokyo