Universität Wien

250118 VO Algebraic number theory (2010S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 19.03. 09:00 - 11:00 Seminarraum
  • Thursday 25.03. 09:00 - 11:00 Seminarraum
  • Friday 26.03. 09:00 - 11:00 Seminarraum
  • Thursday 15.04. 09:00 - 11:00 Seminarraum
  • Friday 16.04. 09:00 - 11:00 Seminarraum
  • Thursday 22.04. 09:00 - 11:00 Seminarraum
  • Friday 23.04. 09:00 - 11:00 Seminarraum
  • Thursday 29.04. 09:00 - 11:00 Seminarraum
  • Friday 30.04. 09:00 - 11:00 Seminarraum
  • Thursday 06.05. 09:00 - 11:00 Seminarraum
  • Friday 07.05. 09:00 - 11:00 Seminarraum
  • Friday 14.05. 09:00 - 11:00 Seminarraum
  • Thursday 20.05. 09:00 - 11:00 Seminarraum
  • Friday 21.05. 09:00 - 11:00 Seminarraum
  • Thursday 27.05. 09:00 - 11:00 Seminarraum
  • Friday 28.05. 09:00 - 11:00 Seminarraum
  • Friday 04.06. 09:00 - 11:00 Seminarraum
  • Thursday 10.06. 09:00 - 11:00 Seminarraum
  • Friday 11.06. 09:00 - 11:00 Seminarraum
  • Thursday 17.06. 09:00 - 11:00 Seminarraum
  • Friday 18.06. 09:00 - 11:00 Seminarraum
  • Thursday 24.06. 09:00 - 11:00 Seminarraum
  • Friday 25.06. 09:00 - 11:00 Seminarraum

Information

Aims, contents and method of the course

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

Assessment and permitted materials

Schriftliche Prüfung am Ende der LV

Minimum requirements and assessment criteria

Familiarity with the basic questions, methods of proof and results in algebraic number theory

Examination topics

Familiarity with the basic questions, methods of proof and results in algebraic number theory

Reading list

Literatur wird in der LV bekanntgegeben. Die Inhalte der LV Algebra
werden vorausgesetzt.

Association in the course directory

MALZ

Last modified: Mo 07.09.2020 15:40