Teoria Álgebrica dos Números - Dirichlet's Unit Theorem - Aula 10

Learn about Dirichlet's unit theorem in this graduate-level mathematics lecture from the 2025 Summer School at 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, cyclotomic fields, and Dirichlet's unit theorem. Study zeta functions and L-series of number fields, along with the analytic class number formula. Drawing from renowned references like Borevich and Shafarevich's Number Theory and Endler's Teoria dos Números Algébricos, gain deep insights into algebraic number theory through this comprehensive lecture delivered in Portuguese by Professor Hossein Movasati.