Arithmetic and Geometry Around Galois Theory

1. Front Matter

   Pages i-xi

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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

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.​  

• Fundamental group
• Galois categories
• Hurwitz space
• Inverse Galois theory
• Stacks

• , 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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