By Joseph H. Silverman

Within the creation to the 1st quantity of The mathematics of Elliptic Curves (Springer-Verlag, 1986), I saw that "the conception of elliptic curves is wealthy, assorted, and amazingly vast," and thus, "many vital issues needed to be omitted." I incorporated a quick advent to 10 extra issues as an appendix to the 1st quantity, with the tacit knowing that at last there may be a moment quantity containing the main points. you're now protecting that moment quantity. it became out that even these ten issues wouldn't healthy regrettably, right into a unmarried publication, so i used to be compelled to make a few offerings. the next fabric is roofed during this booklet: I. Elliptic and modular capabilities for the complete modular team. II. Elliptic curves with complicated multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron versions, Kodaira-Neron type of unique fibers, Tate's set of rules, and Ogg's conductor-discriminant formulation. V. Tate's concept of q-curves over p-adic fields. VI. Neron's thought of canonical neighborhood peak services.

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