By Joseph H. Silverman

The idea of elliptic curves is special through its lengthy historical past and by means of the range of the equipment which have been utilized in its learn. This ebook treats the mathematics procedure in its sleek formula, by utilizing uncomplicated algebraic quantity idea and algebraic geometry. Following a short dialogue of the required algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and international fields. ultimate chapters take care of fundamental and rational issues, together with Siegels theorem and particular computations for the curve Y = X + DX, whereas 3 appendices finish the full: Elliptic Curves in features 2 and three, crew Cohomology, and an summary of extra complex themes.

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