250118 VO Algebraic number theory (2010S)

Historically, Diophantine Equations were the principal motivation for the
development of algebraic number theory. In these lectures we will be
concerned with generalizations of the integral domain of ordinary integers
which are called algebraic integers. By definition, an algebraic integer
is a root of a monic polynomial with integral coefficients. The study of a
suitable ring of algebraic integers will help in the solution of a problem
initially stated in terms of ordinary integers. We will consider various
instances of this phenomenon. List of cotents: integrality, Dedekind domains, class group, quadratic and cubic fields, arithmetic of cyclotomic fields, Gauss’s law of quadratic reciprocity (revisited), laws of decomposition, geometry of numbers, Dirchlet's unit theorem, some Diophantine equations