Projective Modules and Complete Intersections
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1672
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen
1672
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Satya MandaI
Projective Modules and Complete Intersections
Springer
Author Satya MandaI Department of Mathematics University of Kansas Lawrence, Kansas 66045, USA e-mail: [email protected]
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Mandal, Satya: Projective modules and complete intersections / Satya MandaI. Berlin; Heidelberg; New York; Barcelona; Budapest ; Hong Kong ; London; Milan; Paris; Santa Clara ; Singapore; Tokyo : Springer,
1997
(Lecture notes in mathematics; 1672) ISBN 3-540-63564-5
Mathematics Subject Classification (1991): l3-XX, l3C I0 ISSN 0075-8434 ISBN 3-540-63564-5 Springer-Verlag Berlin Heidelberg New York 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Printed in Germany 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: Camera-ready TEX output by the author SPIN: 10553364 46/3142-543210 - Printed on acid-free paper
Preface In these notes we give an account of the developments in research in Projective Modules and Complete Intersections since the proof of Serre's Conjecture due to Quillen and Suslin and the subsequent publication of T-Y Lam's book, Serre's Conjecture. I expect these notes to be accessible to a wide range of readers, with or without a serious background in commutative algebra. These notes evolved out of class notes for a course on this topic that I taught several years ago at the University of Kansas to a group of students who had no prior serious exposure to commutative algebra. My students enjoyed the course. I would hope that the readers will find these notes enjoyable as well. I need to thank a long list of people who helped me, directly or indirectly, to accomplish this goal. I thank Professor Amit Roy of the Tata Institute of Fundamental Research, Bombay, for the excellent training he gave me in my early career. I would also like to thank my friends Daniel Katz and Jeffrey Lang for their encouragement and for many helpful discussions. Thanks are also due to D. S. Nagaraj of the Institute of Mathematical Sci
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