Universität Wien
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250066 VO Algebraic number theory (2013W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.12. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.12. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.12. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 14:00 - 16:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.01. 14:00 - 16:00 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