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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Elkies Aug 7 ’11 at Email Required, but never shown. 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 mordell-weli the large sieve to thin sets.
If you are looking for a proof of the Mordell-Weil theorem in its utmost generality i.
Lectures on the Mordell-Weil Theorem : Jean-Pierre Serre :
That said, I am certainly a fan of Cohen’s exposition as well, and it’s nice to have a lecturess formal reference for this argument.
Check out the top books of the year on our page Best Books of Home Contact Us Help Free delivery worldwide. Clark Aug 7 ’11 at 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. I could hardly imagine less prerequisites than this.
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. See also his yhe survey Diophantine equations with special reference to elliptic curves J. Chevalley-Weil, but I decided to bypass them for various reasons.
Cassels gives a simply beautiful proof of this that takes about two pages. An Introduction” see Part C. Included are applications to, for example, Mordell’s conjecture, the construction of Galois extensions, and the classical class number 1 problem. I found the same proof worked out for a general local field in: Proofs of Mordell-Weil theorem Ask Question.
Description The book is based on a course given by J. 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. Professor, just want to mention a morxell-weil technicality I read in the proof by Manin. I do not really understand his reasoning.
Actually, the wikipedia article you cite cites Joe Silverman’s book, lectres contains such a “pedagogical” exposition. 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.
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, I do think it’s minor.
That’s why the mordell-wril proof is more complicated. I would like to ask if there exist pedagogical expositions of the Mordell-Weil theorem wikipedia.
Those techniques aren’t even that unnatural or obscure: Manifolds and Modular Forms Friedrich Hirzebruch. Of course it is still “pedagogical”, but it seems that the OP is looking for something with minimal prerequisites. Silverman “The arithmetic of elliptic curves” Chapter 8 is about Mordell-Weil.
This group is related to the Selmer group. Manifolds and Modular Forms Rainer Jung.
He makes a beeline to Mordell-Weil and gives a simple, but not overly computational proof, in an impressively short mordell-weil of pages. I am currently teaching a course on elliptic curves, primarily out of Silverman’s first text which is, of course, wonderful.
Lectures on the Mordell-Weil Theorem
Home Questions Tags Users Unanswered. Sign up or log in Sign up using Google. This gives the following simplifications: