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Birkhäuser

L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld

  • Book
  • © 2008

Overview

Authors:
  1. Laurent Fargues

    1. Laboratoire de Mathématiques d’Orsay, Orsay, France

  2. Alain Genestier

    1. Laboratoire de Mathématiques d’Orsay, Orsay, France

  3. Vincent Lafforgue

    1. Centre de Mathématiques de Jussieu, Université Paris 6 Pierre et Marie Curie, Paris, France

  • First book on the subject
  • Complete and thorough proof of the existence of the isomorphism between Lubin-Tate and Drinfeld towers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematics (PM, volume 262)

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  • 42 Citations

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About this book

Ce livre contient une démonstration détaillée et complète de l'existence d'un isomorphisme équivariant entre les tours p-adiques de Lubin-Tate et de Drinfeld. Le résultat est établi en égales et inégales caractéristiques. Il y est également donné comme application une démonstration du fait que les cohomologies équivariantes de ces deux tours sont isomorphes, un résultat qui a des applications à l'étude de la correspondance de Langlands locale. Au cours de la preuve des rappels et des compléments sont donnés sur la structure des deux espaces de modules précédents, les groupes formels p-divisibles et la géométrie analytique rigide p-adique.

This book gives a complete and thorough proof of the existence of an equivariant isomorphism between Lubin-Tate and Drinfeld towers in infinite level. The result is established in equal and inequal characteristics. Moreover, the book contains as an application the proof of the equality between the equivariant cohomology of both towers, a result that has applications to the local Langlands correspondence. Along the proof background and complements are given on the structure of both moduli spaces, p-divisible formal groups and p-adic rigid analytic geometry.

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxii
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  3. Back Matter

    Pages 323-325
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  4. L’isomorphisme des deux tours Une autre approche en égales caractéristiques

    1. Front Matter

      Pages 327-327
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    2. Introduction

      Pages 329-329

    3. Rappels sur les deux tours et énoncé du théorème

      Pages 331-340

    4. Théorémes de représentabilité explicites

      Pages 341-363

    5. Tour de Lubin-Tate et domaines fondamentaux

      Pages 365-370

    6. Réduction aux domaines fondamentaux

      Pages 371-377

    7. Démonstration du théorème IV.1.1

      Pages 379-406
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Authors and Affiliations

  • Laboratoire de Mathématiques d’Orsay, Orsay, France

    Laurent Fargues, Alain Genestier

  • Centre de Mathématiques de Jussieu, Université Paris 6 Pierre et Marie Curie, Paris, France

    Vincent Lafforgue

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Bibliographic Information

  • Book Title: L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld

  • Authors: Laurent Fargues, Alain Genestier, Vincent Lafforgue

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-7643-8456-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2008

  • Hardcover ISBN: 978-3-7643-8455-5Published: 17 December 2007

  • eBook ISBN: 978-3-7643-8456-2Published: 07 May 2008

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XXII, 406

  • Topics: Algebraic Geometry, Number Theory

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