By Joseph H. Silverman

Within the creation to the 1st quantity of The mathematics of Elliptic Curves (Springer-Verlag, 1986), I saw that "the thought of elliptic curves is wealthy, diversified, and amazingly vast," and for this reason, "many very important issues needed to be omitted." I incorporated a quick creation to 10 extra themes as an appendix to the 1st quantity, with the tacit figuring out that at last there should be a moment quantity containing the main points. you're now maintaining that moment quantity. it became out that even these ten subject matters 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 e-book: I. Elliptic and modular services for the entire modular team. II. Elliptic curves with complicated multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron versions, Kodaira-Neron category of distinctive fibers, Tate's set of rules, and Ogg's conductor-discriminant formulation. V. Tate's thought of q-curves over p-adic fields. VI. Neron's conception of canonical neighborhood peak services.

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