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Abelian Varieties - James Milne
www.jmilne.orgIntroduction The easiest way to understand abelian varieties is as higher-dimensional analogues of ellip-tic curves. Thus we first look at the various definitions of an elliptic curve. Fix a ground field kwhich, for simplicity, we take to be algebraically closed. An elliptic curve over k can be defined, according to taste, as: