Kurs: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. For complete notes in Pdf see here.
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 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
Further reading
Forcing algebras, syzygy bundles, and tight closure (Holger Brenner, survey article)
Some remarks on the affineness of -bundles (Holger Brenner, survey article)
A guide to closure operations in commutative algebra (Neil Epstein, survey article)
Tight closure and plus closure in dimension two (Holger Brenner)
On the arithmetic of tight closure (Holger Brenner and Moty Katzman)
Tight closure does not commute with localization (Holger Brenner and Paul Monsky)
Continuous solutions to algebraic forcing equations (Holger Brenner)
Continuous closure, axes closure, and natural closure (Neil Epstein and Mel Hochster)
Continuous closure of sheaves (János Kollár)