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Arithmetic and Geometry Around Galois Theory

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Pierre Dèbes

    1. , Laboratoire Paul Painlevé, Université Lille 1, Villeneuve d'Ascq Cédex, France

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  2. Michel Emsalem

    1. , Laboratoire Paul Painlevé, Université Lille 1, Villeneuve d'Ascq Cédex, France

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  3. Matthieu Romagny

    1. , Institut de Recherche Mathématique de Re, Université Rennes 1, Rennes Cedex, France

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  4. A. Muhammed Uludağ

    1. , Department of Mathematics, Galatasaray University, Beşiktaş, İstanbul, Turkey

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  • Provides the current states of affairs in geometric Galois theory in a number of lecture notes and survey papers
  • Includes introductory lecture notes on stacks
  • Establishes connections of Galois theory with moduli problems ?
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (10 papers)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Algebraic Stacks with a View Toward Moduli Stacks of Covers

    • José Bertin
    Pages 1-148

  3. Models of Curves

    • Matthieu Romagny
    Pages 149-170

  4. Galois Categories

    • Anna Cadoret
    Pages 171-246

  5. Fundamental Groupoid Scheme

    • Michel Emsalem
    Pages 247-286

  6. Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves

    • Niels Borne
    Pages 287-304

  7. On the “Galois Closure” for Finite Morphisms

    • Marco A. Garuti
    Pages 305-325

  8. Hasse Principle and Cohomology of Groups

    • Jean-Claude Douai
    Pages 327-335

  9. Periods of Mixed Tate Motives, Examples, l-adic Side

    • Zdzisłlaw Wojtkowiak
    Pages 337-369

  10. On Totally Ramified Extensions of Discrete Valued Fields

    • Lior Bary-Soroker, Elad Paran
    Pages 371-376

  11. An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups

    • Rolf-Peter Holzapfel, Maria Petkova
    Pages 377-401
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About this book

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul):  "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.​  

Editors and Affiliations

  • , Laboratoire Paul Painlevé, Université Lille 1, Villeneuve d'Ascq Cédex, France

    Pierre Dèbes, Michel Emsalem

  • , Institut de Recherche Mathématique de Re, Université Rennes 1, Rennes Cedex, France

    Matthieu Romagny

  • , Department of Mathematics, Galatasaray University, Beşiktaş, İstanbul, Turkey

    A. Muhammed Uludağ

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