Universität Wien

442504 VO Topics from Number Theory (2019W)

3.00 ECTS (2.00 SWS), SPL 44 - Doktoratsstudium Naturwissenschaften und technische Wissenschaften

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

1.) The course "Topics from number theory" is a
direct continuation of the course "Topics from number theory" from summer semester.

2.) Subject of the course in summer semester were the basics of the
theory of function fields up to Riemann Roch Theorem.
In this semester we will continue the theory of function fields;
planned topics are

- Extensions of function fields and the Riemann Hurwitz formula for the genus

- The Zeta function of function fields

- Geometric interpretation of function fields: algebraic curves

- Introduction to Drinfeld modules

- if time permits: Applications to Coding theory

3.) The course will
assume basic knowledge of the theory of function fields e.g. as
they appeared in "Topics from number theory" from summer semester. Thus,
participants should have a look at
the course from summer semester or equally well at the books recommended in the reading list.

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

To pass the oral exam

Examination topics

The content of the lecture course

Reading list

The following books are the primary references for the course (and also were the main reference for the first part of the course from last semester):

Rosen, M.: "Number Theory in function fields"

Stichtenoth, H.: "Algebraic function fields"

Additional reference:

Artin, E.: "Algebraic Numbers and Algebraic Functions"

Lütkebohmert, W.: "Kodierungstheorie"

One might also look at:

Moreno, C.: "Algebraic curves over finite fields"

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:22