A Course on Derived Categories Academic Article uri icon


  • Date: 7 May 2015. Revised: a few corrections, no major changes. 1 … 12.4. The embedding of M in D(M) … 16.3. Rigid dualizing complexes and perverse coherent sheaves … These are notes for an advanced course given at Ben Gurion University in Spring 2012. In this course I am following various sources, mostly [RD], [Sc], [KS2] and [Wei], but … 0.1. A motivating discussion: duality. By way of introduction to the subject, let us consider duality. Take a field K. Given a K-module M (ie a vector space), let … D : ModA → ModA, D(M) := HomA(M,A) … G ⊕ H, with G free and H finite. It is important to note that this is not a canonical isomorphism: there is a canonical short exact sequence … (We may view the abelian group Q/Z as the group of roots of 1 in C, via the exponential map.) There is a natural transformation η : 1 → D ◦ D , and if H is a finite abelian group then ηH is an isomorphism. So D is a …

publication date

  • January 1, 2012