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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Silverman “The arithmetic of elliptic curves” Chapter 8 is about Mordell-Weil.

And Ireland and Rosen give many references; a student following them gets a very good motivated introduction to Galois cohomology By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. I even found the exposition somewhat better.

Namely, prove weak MW by finiteness of division fields, construct heights and do the descent argument. Tate “The rational points on elliptic curves” is a wonderful introduction to elliptic curves over rational numbers. Post Your Answer Discard By clicking “Post Your Fhe, 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. 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 – Theprem of elliptic curves of large rank – The large sieve – Applications of the large sieve to thin sets.

Email Required, but never shown. For the case of elliptic curves, there is Mordell’s proof, discussed in his book Diophantine Equations pp. 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. Frobenius Manifolds Klas Diederich.

Yuri Zarhin 4, 14 I found the same proof worked out mrodell-weil a general local field in: 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”.

Professor, just want to mention a small technicality I read in the proof by Manin.

Manifolds and Modular Forms Friedrich Hirzebruch. Cassels gives a simply beautiful proof of this that takes about two pages. Skill, Technology and Enlightenment: Here is a quote from this last paper: Capacities in Complex Anaylsis Urban Cegrell. This group is related to the Selmer group.

Chevalley-Weil, but I decided to bypass them for various reasons. Sign up using Email and Password.

This gives the following simplifications: He makes a beeline to Mordell-Weil and gives a simple, but not overly computational proof, in an impressively short span of pages. Elkies Aug 7 ’11 at What parts of number theory algebraic geometry one should better learn first before starting to read a proof of Ob We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book.

Clark Jan 6 ’17 at 4: Included are applications to, for example, Mordell’s conjecture, the construction of Galois extensions, and the classical class number 1 problem.

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

Proofs of Mordell-Weil theorem Ask Question. Description The book is based on a course given by J. Visit our Beautiful Ln page and find lovely books for kids, photography lovers and more.

I think it’s a nice argument. Home Questions Tags Users Unanswered. By using our website you agree to our use of cookies.

## Lectures on the Mordell-Weil Theorem

mordellweil Actually, the wikipedia article you cite cites Joe Silverman’s book, which contains such a “pedagogical” exposition. Clark Aug 7 ’11 at Serre at the Thekrem de France in and Book ratings by Goodreads.

Clark Oct 29 ’12 at Weil’s generalization of Mordell’s theorem and subsequent generalizations was usually referred to as the Mordell-Weil Theorem. 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.

We use cookies to give you the best possible experience. Of course it is still “pedagogical”, but it seems that the OP is looking for something with minimal prerequisites. I am currently teaching a course on elliptic curves, primarily out of Silverman’s first text which is, of course, wonderful. For abelian varieties, you need to know rather a lot of algebraic geometry. I would like to ask if there exist pedagogical expositions of the Mordell-Weil theorem wikipedia. An extensive list of corrections, by the venerable MOer BCnrd, to errors introduced in the TeXed version can be found here math.

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