By Joseph H. Silverman
The idea of elliptic curves is exotic by means of its lengthy background and via the variety of the equipment which have been utilized in its research. This ebook treats the mathematics process in its glossy formula, by utilizing uncomplicated algebraic quantity idea and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields. ultimate chapters take care of crucial and rational issues, together with Siegels theorem and specific computations for the curve Y = X + DX, whereas 3 appendices finish the total: Elliptic Curves in features 2 and three, crew Cohomology, and an outline of extra complicated themes.
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