Voloshyn D. Vector bundles over noncommutative nodal curves

The thesis is devoted to the study of vector bundles over noncommutative curves and derived categories coherent sheaves on noncommutative nodal curves. The structure of nodal algebras over a complete discrete valuation ring with algebraically closed residue field is described. Vector bundles over noncommutative nodal curves of string type and of almost string type are investigated. We prove that in other cases the classification of vector bundles over a noncommutative curve is a wild problem. Derived categories of coherent sheaves over nodal noncommutative curves of string and almost string types are described. Nodal curves of string and almost string types are VB-tame and derived tame.