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Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
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7773.tp.half.pdf 1 10/11/10 9:21 AM NANKAI TRACTS IN MATHEMATICS Series Editors: Yiming Long and Weiping Zhang Chern Institute of Mathematics Published Vol. 1 Vol. 2 Scissors Congruences, Group Homology and Characteristic Classes by J. L. Dupont The Index Theorem and the Heat Equation Method by Y. L.Yu Vol. 3 Least Action Principle of Crystal Formation of Dense Packing Type and Kepler’s Conjecture by W. Y. Hsiang Vol. 4 Lectures on Chern–Weil Theory and Witten Deformations by W. P. Zhang Vol. 5 Contemporary Trends in Algebraic Geometry and Algebraic Topology edited by Shiing-Shen Chern, Lei Fu & Richard Hain Vol. 6 Riemann–Finsler Geometry by Shiing-Shen Chern & Zhongmin Shen Vol. 7 Iterated Integrals and Cycles on Algebraic Manifolds by Bruno Harris Vol. 8 Minimal Submanifolds and Related Topics by Yuanlong Xin Vol. 9 Introduction to Several Complex Variables: Three Methods of Several Complex Variables by Yum-Tong Siu et al. Vol. 10 Differential Geometry and Physics edited by Mo-Lin Ge & Weiping Zhang Vol. 11 Inspired by S S Chern edited by Phillip A. Griffiths Vol. 12 Topology and Physics edited by Kevin Lin, Zhenghan Wang & Weiping Zhang Vol. 13 Etale Cohomology Theory by Lei Fu YeeSern - Etale Cohomology Theory.pmd 2 12/17/2010, 3:13 PM 7773.tp.F.pdf 1 10/11/10 9:20 AM Nankai Tracts in Mathematics – Vol. 13 ETALE COHOMOLOGY THEORY Lei Fu Chern Institute of Mathematics, Nankai University, China Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ETALE COHOMOLOGY THEORY Nankai Tracts in Mathematics — Vol. 13 Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4307-72-7 ISBN-10 981-4307-72-6 Printed in Singapore. YeeSern - Etale Cohomology Theory.pmd 1 12/17/2010, 3:13 PM January 5, 2011 11:3 World Scientific Book - 9in x 6in Preface The manuscript of this book was written in 1998–1999. At that time, I was invited to give a series of talks at the Morningside Center of Mathematics on Deligne’s proof of the Weil conjecture. To prepare the talks, I wrote the book [Fu (2006)] on algebraic geometry covering the main materials in [EGA] I–III, and the current book covering the main materials in [SGA] 1, 4, 4 12 , and 5 related to etale cohomology theory. I hope this bo