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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Chandan Singh Dalawat See also his masterly survey Diophantine equations with special reference to elliptic curves J. There are already eight perfectly fine references in the answers. Yuri Zarhin 4, 14 And Ireland and Rosen give many references; a student following them gets a very good motivated introduction to Galois cohomology I do think it’s minor.

Clark Jan 6 ’17 at 4: I think it’s a nice argument.

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

Silverman “The arithmetic of elliptic curves” Chapter 8 is about Mordell-Weil. Lectures on the Mordell-Weil Theorem. Weil’s generalization of Mordell’s theorem and subsequent generalizations was usually referred to as the Mordell-Weil Theorem.

What parts of number theory algebraic geometry one should better learn first before starting to read a proof of Mordell-Weil? Another text at the theorfm level that covers Mordell’s theorem i. Sign up using Facebook.

The Best Books of 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. Clark Aug 7 ’11 at Especially, there th a part of the proof of Mordell-Weil which is traditionally proved using aspects of the reduction theory of elliptic curves over local fields.

An Introduction” see Part C.

Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Professor, just want to mention a small technicality I read in the proof by Manin. Namely, prove weak Lectjres by finiteness of division fields, construct heights and do the descent argument. This is one of the best books available on the subject, but it is certainly not the easiest. On Practical Philosophy Bo Goranzon. Rational Points Gerd Faltings. Manifolds and Modular Forms Friedrich Hirzebruch.

I found the same proof worked out for a general local field in: 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. Skill, Technology and Enlightenment: Manifolds and Lecctures Forms Rainer Jung. 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.

You should be able to find what you want in online lecture notes. Post as a guest Name. I do not really understand his reasoning.

I wanted to comment that, apart from different emphases on various oon or a choice of heavy machinery vs computation, these are all the same proof.

Silverman devotes an entire chapter to lectuees curves over local fields and another entire chapter to formal groups, to prove the key fact that the kernel of reduction contains no torsion of order prime to the residue characteristic.

Of course it is still “pedagogical”, but it seems that the OP is looking for something with minimal prerequisites.

## Lectures on the Mordell-Weil Theorem

In fact, here are my notes for the course: Table of contents Contents: Serre at the College de France morcell-weil and Description The book is lectres on a course given by J. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you morcell-weil read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

For more advanced treatment of Mordell-Weil, I suggest the following textbook: Product details Format Hardback pages Dimensions x x Tate “The rational points on elliptic curves” is a wonderful introduction to elliptic curves over rational numbers.

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The book is not lecture self-contained, but I am sure the preface explains the prerequisites.

Goodreads is the world’s largest site for readers with over 50 million reviews. Eventually it was translated into English and published as an appendix to Second and Third editions of Mumford’s book. If you are looking for a proof of the Mordell-Weil theorem in its utmost generality i. An extensive list of corrections, by the venerable MOer BCnrd, to errors introduced in the TeXed version can be found here math.

### Lectures on the Mordell-Weil theorem – Jean-Pierre Serre – Google Books

I could hardly imagine less prerequisites than this. 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.

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