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The p-adic Simpson Correspondence (AM-193)$
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Ahmed Abbes, Michel Gros, and Takeshi Tsuji

Print publication date: 2016

Print ISBN-13: 9780691170282

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691170282.001.0001

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Representations of the fundamental group and the torsor of deformations. Global aspects

Representations of the fundamental group and the torsor of deformations. Global aspects

Chapter:
(p.179) Chapter III Representations of the fundamental group and the torsor of deformations. Global aspects
Source:
The p-adic Simpson Correspondence (AM-193)
Author(s):

Ahmed Abbes

Michel Gros

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691170282.003.0003

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

Keywords:   p-adic Simpson correspondence, torsor, deformation, locally irreducible scheme, Koszul complex, additive categories, Faltings ringed topos, adic module, Higgs–Tate algebra, Dolbeault module

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