241014 Local Cohomology (S) (WiSe 2014/2015)

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".

Requirements for participation, required level

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.

Bibliography

Bruns, W, Herzog, J: Cohen-Macaulayrings, Cambridge University Press (1993), ISBN 978-0-521-56674-2.

Hartshorne, Robin (1967) [1961], Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall, 1961, Lecture notes in mathematics 41, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0073971.

Iyengar, Srikanth B.; Leuschke, Graham J.; Leykin, Anton; Miller, Claudia; Miller, Ezra; Singh, Anurag K.; Walther, Uli (2007), Twenty-four hours of local cohomology, Graduate Studies in Mathematics 87, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4126-6.