Lectures on the Mordell-Weil Theorem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | German |
| Published: |
Wiesbaden
Vieweg+Teubner Verlag
1989
|
| Series: | Aspects of Mathematics / Aspekte der Mathematik
E 15 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (X, 220 S.) |
| ISBN: | 9783663140603 9783528089689 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-663-14060-3 |
Staff View
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Record in the Search Index
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| author | Serre, Jean-Pierre 1926- |
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| author_role | aut |
| author_sort | Serre, Jean-Pierre 1926- |
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| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-663-14060-3 |
| format | Electronic eBook |
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| id | DE-604.BV042452256 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:22:07Z |
| institution | BVB |
| isbn | 9783663140603 9783528089689 |
| issn | 0179-2156 |
| language | German |
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| series2 | Aspects of Mathematics / Aspekte der Mathematik |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Lectures on the Mordell-Weil Theorem von Jean-Pierre Serre ; herausgegeben von Martin Brown Wiesbaden Vieweg+Teubner Verlag 1989 1 Online-Ressource (X, 220 S.) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics / Aspekte der Mathematik E 15 0179-2156 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 Mathematics Geometry, algebraic Geometry Algebraic Geometry Mathematics, general Mathematik Mordell-Weil-Theorem (DE-588)4215929-5 gnd rswk-swf Mordell-Vermutung (DE-588)4123793-6 gnd rswk-swf Mordell-Weil-Theorem (DE-588)4215929-5 s 1\p DE-604 Mordell-Vermutung (DE-588)4123793-6 s 2\p DE-604 Brown, Martin Sonstige oth https://doi.org/10.1007/978-3-663-14060-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre 1926- Lectures on the Mordell-Weil Theorem Mathematics Geometry, algebraic Geometry Algebraic Geometry Mathematics, general Mathematik Mordell-Weil-Theorem (DE-588)4215929-5 gnd Mordell-Vermutung (DE-588)4123793-6 gnd |
| subject_GND | (DE-588)4215929-5 (DE-588)4123793-6 |
| title | Lectures on the Mordell-Weil Theorem |
| title_auth | Lectures on the Mordell-Weil Theorem |
| title_exact_search | Lectures on the Mordell-Weil Theorem |
| title_full | Lectures on the Mordell-Weil Theorem von Jean-Pierre Serre ; herausgegeben von Martin Brown |
| title_fullStr | Lectures on the Mordell-Weil Theorem von Jean-Pierre Serre ; herausgegeben von Martin Brown |
| title_full_unstemmed | Lectures on the Mordell-Weil Theorem von Jean-Pierre Serre ; herausgegeben von Martin Brown |
| title_short | Lectures on the Mordell-Weil Theorem |
| title_sort | lectures on the mordell weil theorem |
| topic | Mathematics Geometry, algebraic Geometry Algebraic Geometry Mathematics, general Mathematik Mordell-Weil-Theorem (DE-588)4215929-5 gnd Mordell-Vermutung (DE-588)4123793-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Geometry Algebraic Geometry Mathematics, general Mathematik Mordell-Weil-Theorem Mordell-Vermutung |
| url | https://doi.org/10.1007/978-3-663-14060-3 |
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