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Learn about algebraic number theory in this graduate-level lecture from IMPA's 2025 Summer School, where Professor Hossein Movasati explores the norm of ideals, proves the main Lemma of Minkowski theory, and demonstrates the finiteness of class number. Delve into fundamental concepts including algebraic integers, rings of algebraic integers of number fields, bases and discriminants, prime ideals, class groups, unique factorization, ideal norms, ramification theory, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields with their connection to class number formulas. Drawing from classical texts by Borevich, Shafarevich, Endler, Ribenboim, and Samuel, gain a comprehensive understanding of advanced algebraic number theory principles and their applications.
