Vieweg+teubner Verlag
Lectures on the Mordell-Weil Theorem
Product Code:
9783528089689
ISBN13:
9783528089689
Condition:
New
$87.33
Lectures on the Mordell-Weil Theorem
$87.33
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.
| Author: Jean Pierre Serre |
| Publisher: Vieweg+teubner Verlag |
| Publication Date: Jan 01, 1989 |
| Number of Pages: 220 pages |
| Binding: Paperback or Softback |
| ISBN-10: 3528089687 |
| ISBN-13: 9783528089689 |
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