Universität Wien
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442503 VO Class field theory (2016S)

5.00 ECTS (3.00 SWS), SPL 44 - Doktoratsstudium Naturwissenschaften und technische Wissenschaften

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 03.03. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.03. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.03. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.04. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.04. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.04. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.04. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.05. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.05. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.06. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.06. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.06. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.06. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.06. 12:30 - 13:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The theme of class field theory is to understand the the entity of all abelian extensions L of a given number field K (i.e. L/K is a galois extension with abelian galois group). The central result of the theory is the Artin reciprocity law, which yields a description of the Galois group of an abelian extension L by data which depend on L but which are contained in the base field K. This reciprocity law is a fundamental result of number theory (it includes a generalization of the quadratic reciprocity law to higher degrees) with connections to many methods and areas of mathematics. Accordingly there are very different approaches to a proof (similar to the quadratic reciprocity law).
We want to present a proof that combines analytic and algebraic methods.

The course is a continuation of the course "Algebraische Zahlentheorie" held in WS 2015; hence, prerequisites are basic knowledge of Algebraic number theory.

Assessment and permitted materials

Oral examination

Minimum requirements and assessment criteria

Examination topics

Reading list

Artin, E., Tate, J.: Class field theory
Neukirch, J.: Klassenkorpertheorie
-: Algebraische Zahlentheorie
Lang, S.: Algebraic number theory
Serre, J.-P.: Local fields

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:47