BIREP — Representations of finite dimensional algebras at Bielefeld
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Seminar Local Cohomology (WS 2014/2015) (eKVV: 24104)

Wednesday 10-12 Uhr, in V4-119 (2 SWS) starting at the 15th of October .
Organizer: Prof. Dr. Henning Krause, Prof. Dr. Christopher Voll, Fajar Yuliawan
Content: Local cohomology was invented by Grothendieck in the early 1960s. Roughly speaking, it is a cohomology theory for sheaves on a topological space, which gives local information with respect to a closed subset (by taking the derived functors of sections). There are various versions of this theory and many applications depending on the context (algebra, geometry, topology).

The seminar provides an introduction to this beautiful theory, based to a large extent on the volume "Twenty-four hours of local cohomology".

Programme

At the moment, we plan to cover the following lectures from the book Twenty-four hours of local cohomology.

I. Fundamental notions II. More commutative algebra III. Algebraic geometry IV. Combinatorics applications Further topics

Pre-requisites

The participants of the seminar are supposed to be familiar with basic concept from (commutative and homological) algebra, including the language of rings and modules.

References

[B] Bruns, W. Commutative algebra arising from the Anand-Dumir-Gupta conjectures. Commutative algebra and combinatorics, 4, 1-38, (2007).
[BH] Bruns, W., and Herzog, J. Cohen-Macaulay rings. Cambridge University Press, 1998.
[BIK] Benson, D., Iyengar, S., and Krause, H. A local-global principle for small triangulated categories. arXiv preprint arXiv:1305.1668.
[FI] Foxby, H. B., & Iyengar, S. Depth and amplitude for unbounded complexes. Commutative algebra (Grenoble/Lyon, 2001), 119–137. Contemp. Math, 331.
[H] Hartshorne, R. Local cohomology. A seminar given by A. Grothendieck. Vol. 41. Springer-Verlag, 1967.
[I] Iyengar, S., et al. Twenty-four hours of local cohomology. Vol. 87. American Mathematical Soc., 2007.
[S1] Stanley, R. P. Hilbert functions of graded algebras, Advances in Math. 28 (1978), 57-83.
[S2] Stanley, R. P. Linear diophantine equations and local cohomology, Inventiones Math. 68 (1982), 175-193.