Universität Wien

250060 VO Algebraic number theory (2019W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 09.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.12. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.12. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 13:15 - 14:45 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

One of the major sources for the development of algebraic number theory was the
attempt to generalize the quadratic reciprocity law to higher
power residues. While the quadratic reciprocity law can be formulated entirely in Q, i.e. it
can be formulated using only rational
numbers the formulation of higher reciprocity laws involves n-th roots of unity, i.e. it
necessarily takes place in a finite extension of Q. This creates the need to consider
finite (i.e. algebraic) extensions of Q - the so called
algebraic number fields - in analogy with Q. The goal of algebraic number theory thus is
to extend the essential properties of
the field Q to finite extensions of Q. Briefly, this means
- to find an analogoue in number fields of the ring of integers Z in Q; in particular this analogoue is a ring and it should have some kind of factorization into primes property.
The study of these rings is a fundament of algebraic number theory.
- to find an analogoue of the embedding of Q into R (and also into p-adic fields Q_p); this makes possible to relate algebraic numbers to geometry and analysis.
If time permits we can occasionally touch on aspects of the modern formulation of
algebraic number theory which evolved in connection
with the geometric interpretation of algebraic numbers.
Prerequisites for the course ``Algebraic number theory'' are Algebra 1 and Algebra 2.

Assessment and permitted materials

Written or oral exam

Minimum requirements and assessment criteria

To pass the written or oral exam

Examination topics

Content of the lecture

Reading list

Neukirch "Algebraische Zahlentheorie"
P. Samuel "Algebraic Theory of Numbers"
Koch "Algebraische Zahlentheorie"
Lang "Algebraic number theory"
I. Stewart, D. Tall, Algebraic Number Theory and Fermat's Last Theorem
D.A. Marcus, Number Fields
W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers

Association in the course directory

MALZ

Last modified: Mo 02.11.2020 15:29