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250057 VO Homological Algebra (2011W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Thursday 06.10. 15:00 - 17:00 Seminarraum
Friday 07.10. 13:00 - 15:00 Seminarraum
Thursday 13.10. 15:00 - 17:00 Seminarraum
Friday 14.10. 13:00 - 15:00 Seminarraum
Thursday 20.10. 15:00 - 17:00 Seminarraum
Friday 21.10. 13:00 - 15:00 Seminarraum
Thursday 27.10. 15:00 - 17:00 Seminarraum
Friday 28.10. 13:00 - 15:00 Seminarraum
Thursday 03.11. 15:00 - 17:00 Seminarraum
Friday 04.11. 13:00 - 15:00 Seminarraum
Thursday 10.11. 15:00 - 17:00 Seminarraum
Friday 11.11. 13:00 - 15:00 Seminarraum
Thursday 17.11. 15:00 - 17:00 Seminarraum
Friday 18.11. 13:00 - 15:00 Seminarraum
Thursday 24.11. 15:00 - 17:00 Seminarraum
Friday 25.11. 13:00 - 15:00 Seminarraum
Thursday 01.12. 15:00 - 17:00 Seminarraum
Friday 02.12. 13:00 - 15:00 Seminarraum
Friday 09.12. 13:00 - 15:00 Seminarraum
Thursday 15.12. 15:00 - 17:00 Seminarraum
Friday 16.12. 13:00 - 15:00 Seminarraum
Thursday 12.01. 15:00 - 17:00 Seminarraum
Friday 13.01. 13:00 - 15:00 Seminarraum
Thursday 19.01. 15:00 - 17:00 Seminarraum
Friday 20.01. 13:00 - 15:00 Seminarraum
Thursday 26.01. 15:00 - 17:00 Seminarraum
Friday 27.01. 13:00 - 15:00 Seminarraum

Information

Aims, contents and method of the course

This lecture is intended to deliver an introduction to homological algebra,
as it is needed for algebraic topology, commutative algebra, group theory
and number rtheory. The following chapters are planned:
Module theory (free, projective, flat, divisible and injective modules),
categories and functors (in particular abelian categories), resolutions and
derived functors (projective and injective resolutions, homology, homotopy,
ext-functor, tor-functor), Group homology and cohomology, spectral sequences
(in particular the Hochschild-Lyndon-Serre spectral sequence), and
finally triangulated categories and derived categories.

Assessment and permitted materials

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

Minimum requirements and assessment criteria

Accomplishment of the basic methods of homological algebra needed for the
research group algebra

Examination topics

varying

Reading list

K. S. Brown: Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1994.

H. Cartan, S. Eilenberg: Homological algebra. Princeton University Press, Princeton, NJ, 1999.

I. Gelfand, Y.I. Manin: Methods of homological algebra, Springer, 2003.

P. Hilton; U. Stammbach: A course in homological algebra, Graduate Texts in Mathematics, Springer-Verlag, New York, 1997.

C.A.Weibel: An introduction to homological algebra, Cambridge, 1994.

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40