18.785 Number Theory I, Fall 2016
Number Theory I
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This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
Absolute values, discrete valuations, localization, Dedekind domains, Etale algebras, Dedekind extensions, Ideal Norm, Dedekind-Kummer Theorem, Galois extensions, Frobenius, Artin map, complete fields, Valuation rings, Hensel's lemmas, Krasner's lemma, Haar measures, Minkowski bound, Dirichlet, Unit theorem, Riemann, Zeta function, Kronecker, Weber, Ray Class, Ring of Adeles, Idele group, Chebotarev density theorem
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