Universität Wien
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250030 VO Homological Algebra (2022S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
MIXED
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.03. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.03. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.03. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.03. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.04. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.04. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.04. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.04. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.05. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.05. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.05. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.05. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.05. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 01.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.06. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.06. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.06. 12:30 - 13:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This lecture has the aim to give an introduction to homological algebra,
as it is needed for algebraic topology, commutative algebra, group theory
and number theory. The following topics 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
triangulated categories and derived categories.

Assessment and permitted materials

Written exam after the end of the lecture.

Minimum requirements and assessment criteria

50 % of the points for the written exam.

Examination topics

All topics covered in the lecture.

Reading list

[1] 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.

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

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

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

Association in the course directory

MALV

Last modified: Fr 01.07.2022 07:48