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Explore the fifteenth lecture in a graduate-level Algebraic Number Theory course, delivered in Portuguese by Professor Hossein Movasati at IMPA's Summer School 2025. Delve into advanced topics including algebraic integers, rings of algebraic integers of number fields, bases and discriminants, ideals and prime ideals, class groups and their finiteness, unique factorization, ideal norms, ramification theory, the fundamental equality, quadratic fields and quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields including the analytic class number formula. Study from recommended texts by Borevich and Shafarevich, Endler, Ribenboim, and Samuel while engaging with this comprehensive mathematical exploration that forms part of IMPA's distinguished graduate program.
