Homological Identities for Differential Graded Algebras

Specialeforsvar ved Anne Gregersen

Titel: Homological Identities for Differential Graded Algebras

Abstract: In this thesis, we lift classical results from module and ring theory, to the theory of differential graded algebras and differential graded modules. Among these are the Auslander-Buchsbaum Formula, the Bass Formula and Gap Theorem. Differential graded algebras and DG modules live in the derived triangulated category of DG modules, hence triangulated categories and Verdier localization are introduced. A tool to lifting the main results to the DG case is semi-free resolutions of DG modules. Hence existence of such is considered. Finally we prove that the length of gaps in the sequence of Bass numbers of a DGA is bounded by the amplitude of the DGA

Vejleder: Henrik G. Holm
Censor: Peter Juul Trosborg, N.Zahles Gymnasium