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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Of course it is still “pedagogical”, but it seems that the OP is looking for something with minimal prerequisites. Clark Oct 29 ’12 at By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Weil’s generalization of Mordell’s theorem and subsequent generalizations was usually referred to as the Mordell-Weil Theorem. Lectures on the Mordell-Weil Theorem. Professor, just theore to mention a small technicality I read in the proof by Manin. I wonder if there is a really different proof of MW.

Lectures on the Mordell-Weil Theorem : Jean-Pierre Serre :

Capacities in Complex Anaylsis Urban Cegrell. After reading this proof, I never understood why other proofs looked so complicated. Rational Points Gerd Faltings. Actually, the wikipedia article you cite cites Joe Silverman’s book, which contains such a “pedagogical” exposition.


Home Contact Us Help Free delivery worldwide. 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, 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.

This is one of the best books available on the subject, but it is certainly not the easiest.

Manifolds and Modular Forms Friedrich Hirzebruch. MathOverflow works best with JavaScript enabled. An extensive list of corrections, by the venerable MOer BCnrd, to errors introduced in the TeXed version can be found here math. 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.

Chandan Singh Dalawat Check out the lectres books of the year on our page Best Books of See also his masterly survey Diophantine equations with special reference to elliptic curves J.

I could hardly imagine less prerequisites than this. Silverman “The arithmetic of elliptic curves” Chapter 8 is about Mordell-Weil. I am currently teaching a course on elliptic curves, primarily out of Silverman’s first text which is, of course, wonderful. There are already eight perfectly fine references in the answers. 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 ths to thin sets.


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.

Lectures on the Mordell-Weil Theorem

For the case of elliptic curves, there is Mordell’s proof, discussed in his book Diophantine Equations pp. 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.

I found the same proof worked out for a general local field in: What parts of number theory algebraic geometry one should better learn first before starting to read a proof of Mordell-Weil?

This gives the following simplifications: We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book. And Ireland and Rosen give many references; a student following them gets a very good motivated introduction to Galois cohomology Chevalley-Weil, but I decided to bypass them for various reasons.