Lectures on the Mordell-Weil theorem
著者
書誌事項
Lectures on the Mordell-Weil theorem
（Aspects of mathematics = Aspekte der Mathematik, ; v. E15）
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, 1997
3rd ed
- : pbk
- タイトル別名
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Autour du théorème de Mordell-Weil
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注記
"This is a translation of ... a course given by J.-P. Serre at the Collège de France in 1980 and 1981"--P. v
Publisher varies: Springer Fachmedien Wiesbaden GmbH
Includes bibliography (p. 200-209) and index (p. 210-218)
Appendix (p. 188-199): The class number 1 problem and integral points on modular curves
内容説明・目次
内容説明
The book is based on a course given by J.-P. Serre at the College 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.
目次
Contents: Heights - Nomalized heights - The Mordell-Weil theorem - Mordell's conjecture - Local calculation of normalized heights - Siegel's method - Baker's method - Hilbert's irreducibility theorem - Construction of Galois extensions - Construction of elliptic curves of large rank - The large sieve - Applications of the large sieve to thin sets.
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