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Explore algebraic number theory in this graduate-level mathematics lecture from IMPA's 2025 Summer School, focusing on algebraic integers, rings of algebraic integers in number fields, bases, and discriminants. Learn about ideals, prime ideals, class groups, unique factorization, and ideal norms. Delve into discriminants, different ideals, ramification, and the fundamental equality. Study quadratic fields, quadratic reciprocity law, cyclotomic fields, and Dirichlet's unit theorem. Examine zeta functions, L-series of number fields, and the analytic class number formula. Based on foundational texts by Borevich & Shafarevich, Endler, Ribenboim, and Samuel, advance your understanding of advanced number theory concepts through this comprehensive Portuguese-language mathematics lecture.
