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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