Lectures on the Mordell-Weil Theorem

Jean-P. Serre (Autor)

Buch | Softcover

X, 218 Seiten

2013 | 3. Third Edition 1997
Vieweg & Teubner (Verlag)
978-3-663-10634-0 (ISBN)

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The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.

Professor Jean-Pierre Serre ist ein renommierter französischer Mathematiker am Collège de France, Paris.

1. Summary.- 2. Heights.- 3. Normalised heights.- 4. The Mordell-Weil theorem.- 5. Mordell's conjecture.- 6. Local calculation of normalised heights.- 7. Siegel's method.- 8. Baker's method.- 9. Hilbert's irreducibility theorem.- 10. Construction of Galois extensions.- 11. Construction of elliptic curves of large rank.- 12. The large sieve.- 13. Applications of the large sieve to thin sets.- Appendix: The class number 1 problem and integral points on modular curves.- A.1. Historical remarks.- A.4. Elliptic curves with complex multiplication.- A.5. Modular curves associated to normalisers of Cartan subgroups and their CM integral points.- A.6. Examples.- A.7. The Gel'fond-Linnik-Baker method.

Erscheint lt. Verlag	13.11.2013
Reihe/Serie	Aspects of Mathematics
Übersetzer	Michel Waldschmidt
Zusatzinfo	X, 218 p.
Verlagsort	Wiesbaden
Sprache	englisch
Maße	170 x 244 mm
Gewicht	426 g
Themenwelt	Technik
Schlagworte	Calculation • Construction • Theorem
ISBN-10	3-663-10634-9 / 3663106349
ISBN-13	978-3-663-10634-0 / 9783663106340
Zustand	Neuware