Course description:

The main goal of this reading course is to give an introduction to the arithmetic of the ring of integers in finite extensions of rationals. Using the first 12 sections in the first chapter of Neukirch's book we cover the following topics: Gaussian integers, integrality, ideals, lattices, Minkowski theory, the finiteness of the class number, Dirichlet's theorem on units, extensions of Dedekind domains, Hilbert' ramification theory, cyclotomic fields, localization, orders.