The Grothendieck definition of sheaf cohomology

Other Talks
Wednesday, October 21, 2009 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Farbod Shokrieh – Ga Tech
John Etnyre
As we have seen already, the global section functor is left exact.  To get a long exact sequence, I will first give the construction of derived functors in the more general setting of abelian categories withenough injectives. If time permits, I will then show that for any ringed space the category of all sheaves of Modules is an abelian category with enough injectives, and so we can construct sheaf cohomology as the right derived functors of the global section functor. The relation with Cech cohomology will be studied in a subsequent talk.