Intersections de deux quadriques et pinceaux de courbes de genre 1 I
Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une techniqu
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Olivier Wittenberg Intersections de deux quadriques et pinceaux de courbes de genre 1 Intersections of Two Quadrics and Pencils of Curves of Genus 1
1901
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1901
Olivier Wittenberg
Intersections de deux quadriques et pinceaux de courbes de genre 1 Intersections of two quadrics and pencils of curves of genus 1
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Author Olivier Wittenberg Department of Mathematics, MS 136 Rice University 6100 S. Main Street Houston, TX 77251-1892 USA e-mail: [email protected]; [email protected]
Library of Congress Control Number: 2006939005 Mathematics Subject Classification (2000): Primary: 11G35; Secondary: 14J20, 14J27, 14J26, 11D09, 11D25, 14G05, 14G25, 14D10 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-69137-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-69137-2 Springer Berlin Heidelberg New York DOI 10.1007/3-540-69137-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, 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. Typesetting by the author and SPi using a Springer LATEX macro package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 11961260
VA41/3100/SPi
543210
Note to the English reader In an effort to make the contents of this French-language volume accessible to a wider audience, we have supplemented the original text with an extensive introduction written in English. The idea was the Springer Lecture Notes in Mathematics series editors’, and I am grateful to them for suggesting it. As a side effect, this monograph contains two introductions. They are not translations of each other; rather, they are complementary, in spite of their more than substantial overlap. The emphasis in the English-language introduction is on the context, while the French-language introduction more systematically describes precise results and refers to the existing literature.
Remerciements Le contenu de cet ouvrage reprend celui de ma thèse de doctorat de l’Université Paris-Sud, et j’ai plaisir à remercier encore une fois tous ceux qui ont contribué d’une manière ou d’une autre à son élaborati
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