Lectures on the Mordell-Weil Theorem. Authors: Serre, Jean Pierre. Buy this book . eBook 40,00 €. price for Spain (gross). Buy eBook. ISBN : Lectures on the Mordell-Weil Theorem (Aspects of Mathematics) ( ): Jean-P. Serre, Martin L. Brown, Michel Waldschmidt: Books. 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 and These notes were.
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There are already eight perfectly fine references in the answers.
aic geometry – Proofs of Mordell-Weil theorem – MathOverflow
This gives the following simplifications: Description The book is based on a course given by J. Mordell himself strongly disapproved of this usage and frequently insisted in public and in private that what he had proved should be called Mordell’s Theorem and that everything else could, for his part, be called simply Weil’s Theorem.
Clark Aug 7 ’11 at I found the same proof worked out for a general local field in: An Introduction” see Part C.
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Lectures on the Mordell-Weil theorem – Jean-Pierre Serre – Google Books
Basic techniques in Diophantine geometry are covered, such as heights, the Kectures theorem, Siegel’s and Baker’s theorems, Hilbert’s irreducibility theorem, and the large sieve. Product details Format Hardback pages Dimensions lectres x Those techniques aren’t even that unnatural or obscure: Skill, Technology and Enlightenment: Serre at the College de France in and There are other ways, e.
Table of contents Contents: Lectures on Algebraic Geometry: Check out the top books of the year on our page Best Books of I do think it’s minor. Eventually it was translated into English and published as an appendix to Second and Third editions of Mumford’s book.
There is a very affordable book by Milne Elliptic curvesBookSurge Publishers, Charleston, and a very motivating one by Koblitz Introduction to elliptic curves and modular formsSpringer, New York, Cassels gives a simply beautiful proof of this that takes about two pages. Niels 3, 12 That’s why the general proof is more complicated. Clark Oct 29 o at Book ratings by Goodreads. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite tbe.
Ob, the wikipedia article you cite cites Joe Silverman’s book, which contains such a “pedagogical” exposition. Looking for beautiful books? Visit our Beautiful Books page and find lovely books for kids, photography lovers and more.
Lectures on the Mordell-Weil Theorem
On the other hand one might also object that it’s misleading to use “intrinsic facts from algebraic geometry” without explaining how these naturally generalize explicit techniques going back to Fermat. For elliptic curves over a number field, you need to know the finiteness of the class number and the finite generation of the group of lctures basic facts in algebraic number theory. This is one of the best books available on the subject, but it is certainly not the easiest. The construction of the height paring can be found in Hindry-Silverman, or in [Brian Conrad, http: That said, I am certainly a fan of Cohen’s exposition as well, and it’s nice to have a more formal reference for this argument.
Weil’s generalization of Mordell’s theorem and subsequent generalizations was usually lectutes to as the Mordell-Weil Theorem. I even found the exposition somewhat better. See also his masterly survey Diophantine equations with special reference to elliptic curves J. Manifolds and Modular Forms Friedrich Hirzebruch.
Namely, prove weak MW by finiteness of division fields, construct heights and do the descent argument.