Abstract

In this series of lectures we discuss algebraic vector bundles on schemes and their torsors. The torsors are objects on which a vector bundle acts by translations. An important class of such bundles arise by forcing algebras for an ideal and an element in a ring. Properties of the forcing algebra and the corresponding torsor reflect properties of ideal closure operations like radical, integral closure, tight closure. Tight closure is reflected by the behavior of local cohomology in the forcing algebra. These algebras themselves yield interesting examples for the behavior of local cohomology under arithmetic and geometric deformations.



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