Basic Structures of Function Field Arithmetic
From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volum
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David Goss
Basic Structures of Function Field Arithmetic
,
Springer
David Goss Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210-1174 USA e-mail: [email protected]
LIbrary of Congr •• s Cltaloglng-In-Publlcatlon Data Gass. On I d. 1952BasIC structures of 'unctlon .Ield arlth •• tlc I DavId Gass . p. c •. "Corrected second pr I nt Ing 1998 a' tha • I rst ad I t I on 1996. wh I ch was orIgInally publlshld as volu.1 35 a. tha SIrles ErglbnlsSl dlr Math . . atlk und Ihrer Grenzgeblete. 3. Folga"--T.p . varsa. Includes bIblIographIcal ra'arlncas and Inde •. ISBN 3-540-63541-6 (saftcavlr : alk. paper) 1. F1tlds. AlgebraIc. 2. Arlth .. tlC 'unctlons . 3. Orlnfeld aadule.. I. Tltla. QA274.G686 1996b 512' .74--dc21 97-35573 CIP
Corrected Second Printing 1998 of the First Edition 1996, which was originally published as Volume 35 of the series Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge.
Mathematics Subject Classification (1991): 11G09, 11R58, llT55, 11S40, 11S80, ISBN-13: 978-3-540-63541-3 DOl: 10.1007/978-3-642-61480-4
e-ISBN-13 : 978-3-642-61480-4
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 microfilms or in any other ways. 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. C Springer-Verlag Berlin Heidelberg 1998
Softcover reprint of the hardcover 1st edition 1998 Typesetting: Camera-ready copy produced by the author's output file using a Springer TEX macro package SPIN 11414148 41/3111 - 5 4 3 2 1- Printed on acid-free paper
In memory of KURT
J. EpPLER
Preface
Classical algebraic number theory concerns the properties satisfied by the rational numbers Q and those numbers a which satisfy a polynomial with rational coefficients. It has always been, and remains, a magical subject with the most wonderful and interesting structures one can imagine. The twists and turns of the theory are so subtle that they read like a masterful mystery story. Who in the nineteenth century, for instance, would ever have thought that a solution to Fermat's Last Theorem would arise from the study of elliptic modular functions? Yet this is precisely the way the well known solution due to G. Frey, J.-P. Serre, K. Ribet, R. Taylor and most importantly, A. Wiles, has proceeded. And it is clear that these fantastic results are by no means the end of the line. What ever else may happen, there will certainly be more wonderfully interesting mysteries and results in algebraic number theory in the years to
