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."
General
Imprint: |
Friedrich Vieweg & Sohn Verlagsgesellschaft Mbh
|
Country of origin: |
Germany |
Release date: |
August 1989 |
First published: |
1989 |
Authors: |
Jean-Pierre Serre
|
Dimensions: |
230 x 155 x 12mm (L x W x T) |
Format: |
Paperback
|
Pages: |
232 |
Edition: |
2nd edition |
ISBN-13: |
978-3-528-08968-9 |
Categories: |
Books
|
LSN: |
3-528-08968-7 |
Barcode: |
9783528089689 |
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