Universität Wien

250060 VO Algebraic number theory (2018W)

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 03.10. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 05.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.10. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 12.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.10. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 19.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.10. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 31.10. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.11. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 09.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.11. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 16.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.11. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 23.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.11. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 30.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.12. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 07.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.12. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 14.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.12. 11:30 - 13:30 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.01. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 11.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.01. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 18.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.01. 16:45 - 18:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 25.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.01. 16:45 - 18:15 Seminarraum 11 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"

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 07.09.2020 15:40