Rickard's Morita theorem for derived categories

Abstract

Vi gir, i full detalj, to ulike bevis for Rickards moritateorem for deriverte kategorier. I det første beviset bruker vi et modifisert dobbeltkjedekompleks for å konstruere en ekvivalens mellom de deriverte kategoriene direkte. Deretter utleder vi teorien rundt deriverte kategorier for differensielt graderte algebraer, som vi så bruker for å gi et alternativt bevis for teoremet.

We give, in full detail, two different proofs of Rickard's Morita theorem for derived categories. In the first proof we use a modified double chain complex to construct an equivalence between the derived categories directly. After that, we develop the theory of derived categories of differential graded algebras, which we then use to give an alternate proof of the theorem.