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Derived Categories and Sheaf Cohomology
Seminar by Denis-Charles Cisinski and Christian Dahlhausen in summer term 2018.
Wednesday 10-12, M 104
Contents
Derived categories were introduced by Grothendieck as a natural reformulation and generalisation of the main constructions of homological algebra. They lead to the notion of triangulated categories. The aim of the seminar is to study this notion through examples, via the study of cohomology of sheaves on a space.Here is a programme including several remarks.
Literature
- S.I. Gelfand, Yu. Manin: Methods of homological algebra (second edition), Springer, 2003.
- M. Kashiwara, P. Schapira: Sheaves on Manifolds, Springer, 1994.
- M. Kashiwara, P. Schapira: Categories and sheaves, Springer, 2006.
Talks
| No. | Date | Title | Speaker |
| 0 | 11.04. | Overview | Christian Dahlhausen |
| 1 | 18.04. | Presheaves and sheaves | Catherine Leveke-Lowzow |
| 2 | 25.04. | Sheaves and sheafification | Gabriele Lobbia |
| 3 | 02.05. | Abelian sheaves | Johannes Gawron |
| 4 | 09.05. | Abelian categories | Christoph Treml |
| 5 | 16.05. | Complexes | Kerstin Blomenhofer |
| 6 | 23.05. | Homotopy categories as triangulated categories | Julian Seipel |
| 7 | 30.05. | Localisation of categories | Jonathan Glöckle |
| 8 | 06.06. | Derived categories | PB |
| 9 | 13.06. | Derived functors | Nicolai Palm |
| 10 | 20.06. | Examples of derived functors | Jakob Werner |
| 11 | 27.06. | Direct image with compact support | Dima Shvetsov |
| 12 | 04.07. | Inverse image with compact support | Peter Hanukaev |
| 13 | 25.07. | Poincaré duality | Christian Dahlhausen |
Organisatorial remarks
In order to obtain credits for the course, you shall:- Give a talk of 80 minutes (the remaining 10 minutes are reserved for questions and discussion).
- Be regularly present at the seminar and participate actively (do not hesitate to ask questions if you do not understand something).
- Prepare a handout of one or two pages including the main aspects of your talk as well as some small excercises for the other participants (so that they are encouraged to think about the content of the talk again).
- Submit a written elaboration of your talk of about 5 to 10 pages. This has to be handed in one week before your talk at the latest (as a PDF via email).
- Show up at the latest two weeks before your talk at one of the organisers' office hours with a draft of your elaboration. This serves to clarify questions about your talk.
- Your work will be graded and credited as written in the Prüfungsordnung.