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ARITHMETIC OF ELLIPTIC CURVES

Here are the notes I am taking for Wei Zhang’s ongoing course on the arithmetic of elliptic curves offered at Columbia University in Fall 2014 (MATH G6761: Topics in Arithmetic Geometry). As the course progresses, these notes will be revised. I recommend that you visit my website from time to time for the most updated version. Due to my own lack of understanding of the materials, I have inevitably introduced both mathematical and typographical errors in these notes. Please send corrections and comments to phlee@math.columbia.edu.