Arithmetic and Geometry Around Galois Theory
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)"
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Series Editors Hyman Bass Joseph Oesterlé Yuri Tschinkel Alan Weinstein
Pierre Dèbes Michel Emsalem Matthieu Romagny A. Muhammed Uluda÷ Editors
Arithmetic and Geometry Around Galois Theory
Editors Pierre Dèbes Laboratoire Paul Painlevé Université Lille 1 Villeneuve d’Ascq France Matthieu Romagny Institut de Recherche Mathématique de Rennes Université Rennes 1 Rennes France
Michel Emsalem Laboratoire Paul Painlevé Université Lille 1 Villeneuve d’Ascq France A. Muhammed Uluda÷ Department of Mathematics Galatasaray University Beúiktaú, østanbul Turkey
ISBN 978-3-0348-0486-8 ISBN 978-3-0348-0487-5 (eBook) DOI 10.1007/978-3-0348-0487-5 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953359 © Springer Basel 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.springer.com)
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
J. Bertin Algebraic Stacks with a View Toward Moduli Stacks of Covers . . . . . .
1
M. Romagny Models of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
149
A. Cadoret Galois Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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