Download E-books Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) PDF

By Joseph H. Silverman

Within the advent to the 1st quantity of The mathematics of Elliptic Curves (Springer-Verlag, 1986), I saw that "the idea of elliptic curves is wealthy, different, and amazingly vast," and therefore, "many very important issues needed to be omitted." I integrated a short creation to 10 extra themes as an appendix to the 1st quantity, with the tacit figuring out that finally there can be a moment quantity containing the main points. you're now keeping that moment quantity. it became out that even these ten themes wouldn't healthy regrettably, right into a unmarried ebook, so i used to be compelled to make a few offerings. the subsequent fabric is roofed during this ebook: I. Elliptic and modular features for the complete modular staff. II. Elliptic curves with complicated multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron versions, Kodaira-Neron class of detailed fibers, Tate's set of rules, and Ogg's conductor-discriminant formulation. V. Tate's idea of q-curves over p-adic fields. VI. Neron's idea of canonical neighborhood top features.

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