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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Lectures on the Mordell-Weil Theorem. Professor, just want to mention a small technicality I read in the proof by Manin.
That’s why the general lectres is more complicated. Those techniques aren’t even that unnatural or obscure: This group is related to the Selmer group. Niels 3, 12 The Best Books of I wanted to comment that, apart from different emphases on various parts or a choice of heavy machinery vs computation, these are all the same proof.
I am currently teaching a course on elliptic curves, primarily out of Silverman’s first text which is, of course, wonderful.
aic geometry – Proofs of Mordell-Weil theorem – MathOverflow
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. Weil’s generalization of Lectuers theorem and subsequent generalizations was usually referred to as the Mordell-Weil Theorem. One might object that it can be misleading to use explicit but obscure polynomial identities instead of more intrinsic facts from algebraic geometry, but the text has lots of good remarks and references to go beyond this elementary approach.
See also his masterly survey Diophantine equations with special reference to elliptic curves J. After reading this proof, I never understood why other proofs looked so complicated. I think it’s a nice argument.
Silverman “The arithmetic of elliptic curves” Chapter 8 is about Mordell-Weil. Chevalley-Weil, but I decided to bypass them for various reasons.
Sign up or log in Sign up using Google. If you are looking for a proof of the Mordell-Weil theorem in its utmost generality i. There is a very elementary and self-contained modulo a few things proved earlier in the book proof in Chapter 19 of the book of Ireland and Rosen, “A classical introduction to modern number theory”. Description The book is based on a course given by J. Eventually it was translated into English and published as an appendix to Second and Third editions of Mumford’s book.
Lectures on the Mordell-Weil Theorem
The book is not entirely self-contained, but I am sure the preface explains the prerequisites. And Ireland and Rosen give many references; a student following them gets a very good motivated introduction to Galois cohomology Especially, there is a part of the proof of Mordell-Weil which is traditionally proved using aspects of the reduction theory of elliptic curves over local fields.
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Post as a guest Name. Rational Points Gerd Faltings. Book ratings by Goodreads. He makes a beeline to Mordell-Weil and gives a simple, but not overly computational proof, in an impressively short span of pages.
Email Required, but never shown. An extensive list of corrections, by the venerable MOer BCnrd, to errors introduced in the TeXed version can be found here math. Clark Oct 29 ’12 at I could hardly imagine less prerequisites than this.
I cleaned up the wikipedia link. Of course it is still “pedagogical”, but it seems that the OP is mordell-wril for something with minimal prerequisites. There are other ways, e.
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, 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.
Another text at the undergraduate level that covers Mordell’s theorem i.
Lectures on the Mordell-Weil Theorem : Jean-Pierre Serre :
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 units basic facts in algebraic number theory. For the case of elliptic curves, there is Mordell’s proof, discussed in his book Diophantine Equations pp. On Practical Philosophy Bo Goranzon.
Yuri Zarhin 4, 14 Clark Jan 6 theorwm at 4: Included are applications to, for example, Mordell’s conjecture, the construction of Galois extensions, and the classical class number 1 problem. You should be able to find what you want in online lecture notes. Table of contents Contents: Manifolds and Modular Forms Friedrich Hirzebruch.