Overview

"This is a translation of ""Auto ur du theoreme de Mordell-Weil"", a course given by J . -P. Serre at the College de France in 1980 and 1981. These notes were originally written weekly by Michel Waldschmidt and have been reproduced by Publications Mathematiques de l'Universite de Paris VI, by photocopying the handwritten manuscript. The present translation follows roughly the French text, with many modi- fications and rearrangements. We have not tried to give a detailed account of the new results due to Faltings, Raynaud, Gross-Zagier . . .; we have just mentioned them in notes at the appropriate places, and given bibliographical references. Paris, Fall 1988 M. L. Brown J. -P. Serre VII CONTENTS 1. Summary. 1 1. 1. Heights. 3 1. 2. The Mordell-Weil theorem and Mordell's conjecture. 3 1. 3. Integral points on algebraic curves. Siegel's theorem. 4 1. 4. Balcer's method. 5 1. 5. Hilbert's irreducibility theorem. Sieves. 5 2. Heights. 7 2. 1. The product formula. 7 2. 2. Heights on Pm(K). 10 2. 3. Properties of heights. 13 2. 4. Northcott's finiteness theorem. 16 2. 5. Quantitative form of Northcott's theorem. 17 2. 6. Height associated to a morphism rj; X -t P . 19 n 2. 7. The group Pic(X). 20 2. 8. Heights and line bundles. 22 2. 9. hc = 0(1) {: } c is of finite order (number fields). 24 2. 10. Positivity of the height. 24 2. 11. Divisors algebraically equivalent to zero."

Full Product Details

Author:   Jean Pierre Serre
Publisher:   Springer Fachmedien Wiesbaden
Imprint:   Vieweg+Teubner Verlag
Edition:   2nd edition
Volume:   E 15
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.361kg
ISBN:  

9783528089689

ISBN 10:   3528089687
Pages:   220
Publication Date:   01 January 1989
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   German

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