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Learn about cyclotomic fields in this graduate-level mathematics lecture from the 2025 Summer School at the Institute of Pure and Applied Mathematics (IMPA). Explore algebraic integers, the ring of algebraic integers of a number field, bases and discriminants, ideals, prime ideals, class groups, and the finiteness of class groups. Delve into unique factorization, prime ideals, ideal norms, discriminants, different and ramification, fundamental equality, quadratic fields, quadratic reciprocity law, and cyclotomic fields. Study Dirichlet's unit theorem, zeta functions, L-series of number fields, and the analytic class number formula. Drawing from renowned references by Borevich & Shafarevich, Endler, Ribenboim, and Samuel, gain deep insights into algebraic number theory through this comprehensive lecture delivered in Portuguese by Professor Hossein Movasati.
