Vector bundles, forcing algebras and local cohomology (Medellin 2012)

This is a short course on vector bundles and their torsors given by Holger Brenner at the Universidad Nacional de Colombia in Medellín in February/March 2012.

Lecture 1 - Linear equations

Lecture 2 - Forcing algebras and closure operations

Lecture 3 - Vector bundles and their torsors

Lecture 4 - Torsors and forcing algebras

Lecture 5 - Tight closure and solid closure

Lecture 6 - Affineness

Lecture 7 - Plus closure and superheight

Lecture 8 - The projective setting, stability

Lecture 9 - Tight closure and plus closure in dimension two

Lecture 10 - Arithmetic and geometric deformations