By Joseph H. Silverman
The idea of elliptic curves is wonderful via its lengthy heritage and through the range of the tools which were utilized in its examine. This e-book treats the mathematics technique in its smooth formula, by utilizing uncomplicated algebraic quantity idea and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields. ultimate chapters care for essential and rational issues, together with Siegels theorem and specific computations for the curve Y = X + DX, whereas 3 appendices finish the complete: Elliptic Curves in features 2 and three, workforce Cohomology, and an summary of extra complicated issues.
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