Universität Wien

250061 VO Algebraic number theory (2014W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 06.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.10. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.11. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 01.12. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.12. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.12. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.12. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.12. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.01. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Number theory is an area in mathematics dealing with properties
of integers in the broadest sense. Algebraic number theory studies
the arithmetic of algebraic number fields — the ring of integers
in the number field, the ideals and units in the ring of integers,
the extent to which unique factorization holds, and so on.
Among other things, the theory arose out of the study of
Diophantine equations.

The chapters are as follows:

Chapter 1: Integral ring extensions, in particular global fields and their
rings of interegs, norm, trace and discriminant.

Chapter 2: Ideals in Dedekind rings, fractional ideals, ideal class group,
unique factorization.

Chapter 3: Finiteness of the class number, Minkowski-Theory,
rings of integers as lattices, special case calss number $1$ fields.

Chapter 4: Dirichlet's Unit Theorem, the analytic class number formula.

Chapter 5: Decomposition and ramification, in general and for Galois
extensions. Ramification and discriminant.

Chapter 6: Cyclotomic fields and their rings of integers, units, and the
Fermat equation.

Chapter 7: Absolute values and local fields, completions, the adelic
viewpoint.

Assessment and permitted materials

Written exam or oral exam after the end of the lecture.

Minimum requirements and assessment criteria

Examination topics

Reading list

BUR] D. Burde, Commutative Algebra, 2009.
[COH] H. Cohen, A course in computational algebraic number theory, 1993.
[KOC] H. Koch, Algebraic number theory, 1997.
[LAN] S. Lang, Algebraic number theory, 1994.
[NEU] J. Neukirch, Algebraic number theory, 1999.
(WAS] L. C. Washington, Introduction to cyclotomic fields, 1997.

Association in the course directory

MALZ

Last modified: Mo 07.09.2020 15:40