Independent Studies in Algebraic Number Theory — IAN

  • Instructor: Dr. Péter MAGA
  • Contact: maga dot peter at renyi dot hu
  • Prerequisites: introductory number theory: primes, fundamental theorem of arithmetic, congruences; abstract algebra: a solid background in the field of abstract algebra up to the notion of groups, rings, fields and modules is an absolute must, field extensions up to the fundamental theorem of Galois theory.
  • Text: Neukirch: Algebraic Number Theory

Course description: This course provides an introduction to the classical theory of algebraic numbers. The class is a reading one, students are expected to read the first twelve sections of the first chapter in Neukirch's book titled Algebraic Number Theory.

Topics covered: Gaussian integers, integrality, ideals, lattices, Minkowski theory, the class number, Dirichlet's unit theorem, extensions of Dedekind domains, Hilbert's ramification theory, cyclotomic fields, localization, orders.

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