In the this thesis, we define and study integrable covariant derivatives and connections on modules over general algebras over a given ground field of characteristic 0. We also study the monodromy of such covariant derivatives or connections.
A large part of the thesis consists of explicit calculations in the following special case: The ring A is the affine coordinate ring of the plane curve corresponding to the simple singularity E_6, and M is any indecomposable, maximal Cohen-Macaulay module over A. We show that in this case, integrable covariant derivatives always exist and we calculate them explicitly. When the ground field is the complex numbers, we also calculate their monodromy.
This thesis is written in norwegian. For an english version, see the (unpublished) manuscript Connections and monodromy on modules. This paper is also more complete, and contains more calculations.
This thesis was submitted for the degree Candidatus Scientiarum in mathematics at the Department of Mathematics, University of Oslo in November 1994. Professor Olav Arnfinn Laudal was the thesis supervisor.
The thesis was defended on December 16th 1994. The external examiner of the thesis was professor Trygve Johnsen, University of Bergen. The examiner accepted the defence for the degree Candidatus Scientarium.