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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This group is related to the Selmer group. 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 to go beyond this elementary approach. I wonder if there is a really different proof of MW.
Anar Akhmedov 4.
I am currently teaching a course on elliptic curves, thw out of Silverman’s first text which is, of course, wonderful. Eventually it was translated into English mordell-wei, published as an appendix to Second and Third editions of Mumford’s book. 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. An Introduction” see Part C. Frobenius Manifolds Klas Diederich.
aic geometry – Proofs of Mordell-Weil theorem – MathOverflow
Clark Oct 29 ’12 at 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. 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.
What parts of number theory algebraic geometry one should better learn first before starting to read a proof of Mordell-Weil? Product details Format Hardback pages Dimensions x x The book is not entirely self-contained, but I am sure the preface explains the prerequisites. Of course it is still “pedagogical”, but it lectires that the OP is looking for something with minimal prerequisites.
Lectures on the Mordell-Weil theorem – Jean-Pierre Serre – Google Books
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. The construction of the height paring can be found in Hindry-Silverman, or in [Brian Conrad, http: I did not say Silverman had the BEST possible proof indeed, I am 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.
On Practical Philosophy Bo Goranzon. 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”.
See also his masterly survey Diophantine equations with special reference to elliptic curves Mordell-eil. Manifolds and Modular Forms Friedrich Hirzebruch. Email Required, but never shown.
Especially, there is a part of the thforem of Mordell-Weil which is traditionally proved using aspects of the reduction theory of elliptic curves over local fields. Goodreads is the world’s largest site for readers with over 50 million reviews. Those techniques aren’t even that unnatural or obscure: 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 do think it’s minor.
Lectures on the Mordell-Weil Theorem
For more advanced treatment of Mordell-Weil, I suggest the following textbook: I do not really understand his reasoning. Book ratings by Goodreads.
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, That’s why the general proof is more complicated. Here is a quote from this last paper: And Ireland and Rosen give many references; a student following them gets a very good motivated introduction to Galois cohomology Silverman devotes an 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.
Skill, Technology and Enlightenment: Which is why I said “might” and “can” Sign up using Email and Password. Description The book is based on a course given by J.