Course Code : | 2600WETHOM |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Wendy Lowen |

At the start of this course the student should have acquired the following competences:

an active knowledge of

- competences corresponding the final attainment level of secondary school

an active knowledge of

- English

Bachelor level algebra course

Some familiarity with basic notions from category theory is an asset

- - The student has processed the basic notions of homological algebra. - He/she is capable of making proofs and solving exercises (for instance from the handbook 'An introduction to homological algebra') independently. - He/she can apply the internalised techniques to the in-depth study of a specific (co)homology theory.

In the first part of the course classical homological algebra is developed within the framework of abelian categories. This involves the following topics: chain complexes, homotopy and homology, injective and projective resolutions, derived functors, Tor and Ext (especially in the context of abelian groups and modules).

The second part of the course consists of the in-depth study of homological methods in some specific topological, algebraic or geometric contexts. Possible topics include:

- homological dimensions in algebra
- group (co)homology, Lie algebra (co)homology
- Hochschild (co)homology of algebras
- simplicial methods and the link with algebraic topology
- sheaf cohomology in de algebraic geometry
- derived and triangualted categories

Class contact teachingLectures Seminars/Tutorials

Directed self-study

Directed self-study

ExaminationWritten with oral presentation Closed book

- Syllabus
- C. A. Weibel, An introduction to homological algebra

The following study material can be studied voluntarily:

- S. I. Gelfand, Y. I. Manin, Methods of Homological algebra

Wendy Lowen: wendy.lowen@uantwerpen.be

Julia Ramos González : julia.ramosgonzalez@uantwerpen.be