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Learn about algebraic number theory in this graduate-level mathematics lecture focusing on Dedekind domains and the ring of integers in number fields. Explore fundamental concepts including algebraic integers, number field integer rings, bases, discriminants, prime ideals, class groups, unique factorization, ideal norms, ramification, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields with class number formulas. Part of IMPA's 2025 Summer School series, this lecture draws from classical texts by Borevich, Shafarevich, Endler, Ribenboim, and Samuel to deliver an in-depth exploration of advanced number theory concepts.
