Periods and Nori Motives
This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then
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Annette Huber Stefan Müller-Stach
Periods and Nori Motives With contributions by Benjamin Friedrich and Jonas von Wangenheim
Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge
A Series of Modern Surveys in Mathematics
Editorial Board L. Ambrosio, Pisa V. Baladi, Paris G.-M. Greuel, Kaiserslautern M. Gromov, Bures-sur-Yvette G. Huisken, Tübingen J. Jost, Leipzig J. Kollár, Princeton G. Laumon, Orsay U. Tillmann, Oxford J. Tits, Paris D.B. Zagier, Bonn
For further volumes: http://www.springer.com/series/728
Volume 65
Annette Huber • Stefan Müller-Stach
Periods and Nori Motives
With contributions by Benjamin Friedrich and Jonas von Wangenheim
123
Annette Huber Mathematisches Institut Albert-Ludwigs-Universität Freiburg Freiburg Germany
Stefan Müller-Stach Institut für Mathematik Johannes Gutenberg-Universität Mainz Mainz Germany
ISSN 0071-1136 ISSN 2197-5655 (electronic) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISBN 978-3-319-50925-9 ISBN 978-3-319-50926-6 (eBook) DOI 10.1007/978-3-319-50926-6 Library of Congress Control Number: 2016960728 Mathematics Subject Classification (2010): 11J81, 11G99, 14C15, 14F20, 14F42, 14F45, 14L15, 16G20, 18E99, 19E15, 32G15, 32G20, 55N35 © Springer International Publishing AG 2017 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
Part I 1
2
Background Material . . . . . . . . . . . . . . . . . . .
3 3 3 4 5 5 6 6 7 8 9 10 11 13 15 20 22 23 24
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27
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31 31 34 36 41 45
General Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Linearising the Category of Varieties . 1.1.2 Divisors with Normal Crossings . . . . . 1.2 Compl
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