Avsnittsöversikt

  • For a scheme X, we introduced and compared  D^b(X)=D^b(\mathrm{Coh} X), D_{\mathrm{Coh}}^b(\mathrm{QCoh} X), D_{\mathrm{QCoh}}(\mathrm{Mod}_{\mathcal{O}_X}) etc. We discussed derived functors for schemes: new ones such as global sections, push-forward, pull-back; and old ones such as Hom and tensor. Composition of push-forward and acyclic/flabby sheaves. Finiteness of push-forward. We also briefly discussed supports of objects in D^b(X).

    In the lecture notes below, there are more material on pull-backs and supports than in the lecture. In the lecture, Lf^* was only briefly defined and for supports, the lemma Supp(Lf^*F) = f^{-1}Supp(F) was stated but not proven and Lemma 3.9 was completely omitted.