Arithmetic and Geometry Around Galois Theory
By: edited by Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ
Contributors: Emsalem, Michel; Romagny, Matthieu; Uludağ, A. Muhammed; SpringerLink (Online service)
Series: Progress in Mathematics -- 304
Publisher: Springer Basel; Imprint: Birkhäuser
Published: 2013
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 401
ISBN-13: 9783034804875
Subjects: Group theory; Group Theory and Generalizations; Field Theory and Polynomials; Mathematics; Algebraic Geometry; Field theory (Physics)
Description: 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.
Table of contents: title: Preface; title: J. Bertin: Algebraic stacks with a view toward moduli stacks of covers; title: M. Romagny: Models of curves; title: A. Cadoret: Galois categories:- M. Emsalem. Fundamental groupoid scheme; title: N. Borne: Extension of Galois groups by solvable groups, and application to fundamental groups of curves; title: M.A. Garuti: On the “Galois closure” for finite morphisms; title: J.-C. Douai: Hasse Principle and Cohomology of Groups; title: Z. Wojtkowiak: Periods of mixed Tate motives, examples, l-adic side; title: L. Bary-Soroker and E. Paran: On totally ramified extensions of discrete valued fields; title: R.-P. Holzapfel and M. Petkova: An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups.