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A vaguely defined branch of mathematics dealing with Varieties, the Mordell Conjecture, Arakelov Theory, and Elliptic Curves.
References
Cornell, G. and Silverman, J. H. (Eds.). Arithmetic Geometry. New York: Springer-Verlag, 1986.
Lorenzini, D. An Invitation to Arithmetic Geometry. Providence, RI: Amer. Math. Soc., 1996.