Paper · May 3, 2017

Simple connexité des fibres d'une application d'Abel-Jacobi et corps de classe local

Laurent Fargues

math.AGarXiv:1705.01526
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Abstract

We give a geometric Langlands type proof of the geometrization conjecture of the local Langlands correspondence introduced by the author for GL_1. For this we study an Abel-Jacobi morphism. We prove that this morphism is a pro-étale locally trivial fibration in simply connected diamonds in high degree. Those diamonds are absolute punctured Banach-Colmez spaces that we study in details.

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Submitted
May 3, 2017
Subjects
math.AG

Comments: in French

Geometrization

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Geometrization of the local Langlands correspondence: an overview (Laurent Fargues, 2016)1Fargues 2016 Etale cohomology of diamonds (Peter Scholze, 2017)2Scholze 2017 Higgs bundles and geometric structures on manifolds (Daniele Alessandrini, 2018)6Alessandrini 2018 Uniform models and short curves for random 3-manifolds (Peter Feller, Alessandro Sisto and Gabriele Viaggi, 2019)7Feller 2019 Canonical geometrization of orientable 3-manifolds defined by vector-colourings of 3-polytopes (Nikolai Erokhovets, 2020)3Erokhovets 2020 Geometrization in Geometry (Izabella Muraro de Freitas and Álvaro Krüger Ramos, 2022)5de Freitas 2022 Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds (Zheng Huang, Longzhi Lin and Zhou Zhang, 2023)8Huang 2023 A Lean Formalization of the Hamilton–Perelman Proof of Thurston's Geometrization Conjecture (Yuan Liao, Ziyang Qin, Jui-Hui Chung et al., 2026)4Liao 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Geometrization of the local Langlands correspondence: an overview

    Laurent Fargues

    Topics Geometrization · Same author Laurent Fargues · Shared terms “Langlands”, “correspondence”, “geometrization conjecture”

  2. Etale cohomology of diamonds

    Peter Scholze

    Topics Geometrization · Shared terms “Langlands”, “geometrization conjecture”, “correspondence”

  3. Canonical geometrization of orientable -manifolds defined by vector-colourings of -polytopes

    Nikolai Erokhovets

    Topics Geometrization · Shared terms “geometrization conjecture”

  4. A Lean Formalization of the Hamilton–Perelman Proof of Thurston's Geometrization Conjecture

    Yuan Liao, Ziyang Qin, Jui-Hui Chung et al.

    Topics Geometrization · Shared terms “geometrization conjecture”

  5. Geometrization in Geometry

    Izabella Muraro de Freitas and Álvaro Krüger Ramos

    Topics Geometrization

  6. Higgs bundles and geometric structures on manifolds

    Daniele Alessandrini

    Topics Geometrization · Shared terms “geometrization conjecture”

  7. Uniform models and short curves for random 3-manifolds

    Peter Feller, Alessandro Sisto and Gabriele Viaggi

    Topics Geometrization · Shared terms “geometrization conjecture”

  8. Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds

    Zheng Huang, Longzhi Lin and Zhou Zhang

    Topics Geometrization

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Geometrization Thurston's conjecture: every closed 3-manifold can be cut along spheres and tori into pieces that each carry one of eight model geometries. Start with: Three dimensional manifolds, Kleinian groups and hyperbolic geometry (Thurston, 1982)

In the guidebook

  1. 10A.2
    Finite Rotation Groups and Spherical Space FormsBook 10A · Three-Manifolds and Geometrization

    Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.

  2. 10A.8
    Thurston’s Eight GeometriesBook 10A · Three-Manifolds and Geometrization

    The model geometries, the geometrization conjecture, and why it implies Poincaré.

  3. 10A.9
    Hyperbolic Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    Ideal tetrahedra, Mostow rigidity, and the thick–thin decomposition.