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250043 VO Selected topics in algebraic: Cohomology of groups (2009W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Monday 05.10. 15:00 - 17:00 Seminarraum
Friday 09.10. 13:00 - 15:00 Seminarraum
Monday 12.10. 15:00 - 17:00 Seminarraum
Friday 16.10. 13:00 - 15:00 Seminarraum
Monday 19.10. 15:00 - 17:00 Seminarraum
Friday 23.10. 13:00 - 15:00 Seminarraum
Friday 30.10. 13:00 - 15:00 Seminarraum
Friday 06.11. 13:00 - 15:00 Seminarraum
Monday 09.11. 15:00 - 17:00 Seminarraum
Friday 13.11. 13:00 - 15:00 Seminarraum
Monday 16.11. 15:00 - 17:00 Seminarraum
Friday 20.11. 13:00 - 15:00 Seminarraum
Monday 23.11. 15:00 - 17:00 Seminarraum
Friday 27.11. 13:00 - 15:00 Seminarraum
Monday 30.11. 15:00 - 17:00 Seminarraum
Friday 04.12. 13:00 - 15:00 Seminarraum
Monday 07.12. 15:00 - 17:00 Seminarraum
Friday 11.12. 13:00 - 15:00 Seminarraum
Monday 14.12. 15:00 - 17:00 Seminarraum
Friday 18.12. 13:00 - 15:00 Seminarraum
Friday 08.01. 13:00 - 15:00 Seminarraum
Monday 11.01. 15:00 - 17:00 Seminarraum
Friday 15.01. 13:00 - 15:00 Seminarraum
Monday 18.01. 15:00 - 17:00 Seminarraum
Friday 22.01. 13:00 - 15:00 Seminarraum
Monday 25.01. 15:00 - 17:00 Seminarraum
Friday 29.01. 13:00 - 15:00 Seminarraum

Information

Aims, contents and method of the course

Group homology and cohomology has its origin in topology. With the rise of
the algebraic methods the homology and cohomology of several algebraic systems
was defined and explored.
We start the lecture by giving an elementary definition of group cohomology,
along with group extensions and factor systems. We give interpretations of
the n-th cohomology group for small n.
Then we study profinite groups and their cohomology, with coefficients
being discrete modules. These groups arise as Galois groups of
(possibly infinite) field extensions. Their cohomology is named Galois
cohomology, and is very important for number theory.
Finally we plan a short account on the functorial definition of cohomology.

Assessment and permitted materials

Written exam or oral exam after the end of the lecture.

Minimum requirements and assessment criteria

familiarity with advanced results and methods of algebra and number theory

Examination topics

varying

Reading list

[SER] Serre, J.-P., Galois cohomology. Springer Verlag 1997.
[WEI] Weibel, C. A., An introduction to homological algebra. Cambridge University Press 1997.
[WES] Weiss, E., Cohomology of groups. Pure and Applied Mathematics, 34 Academic Press 1969.
[CAE] Cartan, E., Eilenberg, S.: Homological algebra. 1956.
[CHE] Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. 1948.
[KNA] Knapp, A. W.: Lie groups, Lie algebras, and cohomology. 1988.

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40