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 : Jean-Pierre Serre :

Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. 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 lecrures go beyond this elementary approach. After reading this proof, I never understood why other proofs looked so complicated.

For the case of elliptic curves, there is Mordell’s proof, discussed in his book Diophantine Equations pp. We use cookies to give you the best possible experience.

That’s why the general proof is more complicated. 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, Anar Akhmedov 4. Of course it is still “pedagogical”, but it seems that the OP is looking for something with minimal prerequisites.

This gives the following simplifications: I do think it’s minor. I wonder if there is a really different proof of MW. Silverman devotes motdell-weil entire chapter to elliptic 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.


By using our website you agree to our use of cookies. Namely, prove weak MW by finiteness of division fields, construct heights and do the descent argument. Eventually it was translated into English and published as an appendix to Second and Third editions tye Mumford’s book. Product details Format Hardback pages Dimensions x x Sign up using Facebook.

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

I mordell-wfil currently teaching a course on elliptic curves, primarily out of Silverman’s first text which is, of course, wonderful. 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. Clark Oct 29 ’12 at Other books in this series. Skill, Technology and Enlightenment: Serre at the College de France in and Yuri Zarhin 4, 14 Email Required, but never shown.

Lectures on the Mordell-Weil Theorem

For abelian varieties, you need to know rather a lot of algebraic geometry. See also his masterly survey Diophantine equations with special reference to elliptic curves J. On Practical Philosophy Lectudes Goranzon. Number Theory and Cryptography” see Chapter 8. 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. Actually, the wikipedia article you cite cites Joe Silverman’s book, which contains such a “pedagogical” exposition.

I did not say Silverman had the BEST possible proof indeed, I mordell-well sure opinions vary on what the best proof is ,but it IS pedadgogical, which is all the OP asked for, and the reference was staring him in the face since he was quoting the wiki article. Included are applications to, for example, Mordell’s conjecture, the construction of Galois extensions, and kordell-weil classical class number 1 problem.


I think it’s a nice argument.

What parts of number theory algebraic geometry one should better learn first before starting to read a proof of Mordell-Weil? Proofs of Mordell-Weil theorem Ask Question.

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Clark Jan 6 ’17 at 4: Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that lectues have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. The book is not entirely self-contained, but I am sure the preface explains the prerequisites. Book ratings by Goodreads. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book.

Elkies Aug 7 ’11 at 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.

If you are looking for a proof of the Mordell-Weil theorem in its utmost generality i. The construction of the height paring can be found in Hindry-Silverman, or in [Brian Conrad, http: Here is a quote from this last paper: There are already eight perfectly fine references in the answers.