Coherent Cohomology, spring 2014

Organization

The seminar will meet weekly on Wednesday 11.00–13.00 in room 409 of the Snellius building. The first meeting is on February 26.

For any questions regarding the seminar, please contact Wouter Zomervrucht.

February 26	Wouter Zomervrucht	Introduction and preliminaries (notes).
March 5	Giulia Battiston	The Leray spectral sequence (notes, references).
March 12		—no seminar—
March 19	Wouter Zomervrucht	Proper pushforward of coherent sheaves (notes).
March 26	Maxim Mornev	Derived categories (notes).
April 2	Christophe Debry	Grothendieck-Serre duality.
April 9	Alexander Tonkelaar	Classical Brown representability (notes).
April 16	Maxim Mornev	Brown representability in triangulated categories (notes).
April 23	Jinbi Jin	The dualizing complex and Grothendieck-Serre duality (notes).
April 30	Niels Lindner	Taming the dualizing complex (notes).
—
October 10	Lenny Taelman	The Woods-Hole trace formula.

The final lecture is on a Friday, 11.00–13.00, in room 401. Expanded notes can be found in the appendix of Sheaves and functions modulo p.

Grothendieck-Serre duality.
A generalization of Serre duality to e.g. proper morphisms. A good reference is Hartshorne's Residues and Duality, as well as Deligne's appendix to that book. We take a more modern approach following Neeman.
Woods-Hole trace formula.
A version of the Lefschetz fixed-point theorem in the setting of coherent cohomology. See SGA 5, III.6.12.