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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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Facsimile : A p-adic Simpson correspondence

Facsimile : A p-adic Simpson correspondence

(p.577) Facsimile : A p-adic Simpson correspondence
The p-adic Simpson Correspondence (AM-193)

Gerd Faltings

Princeton University Press

This chapter presents the facsimile of Gerd Faltings' article entitled “A p-adic Simpson Correspondence,” reprinted from Advances in Mathematics 198(2), 2005. In this article, an equivalence between the category of Higgs bundles and that of “generalized representations” of the étale fundamental group is constructed for curves over a p-adic field. The definition of “generalized representations” uses p-adic Hodge theory and almost étale coverings, and it includes usual representations which form a full subcategory. The equivalence depends on the choice of an exponential function for the multiplicative group. The method used in the proofs is the theory of almost étale extensions. A nonabelian Hodge–Tate theory is also developed.

Keywords:   p-adic Simpson correspondence, Gerd Faltings, Higgs bundle, étale fundamental group, generalized representation, p-adic Hodge theory, almost étale covering, almost étale extension, Hodge–Tate theory

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