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 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

Further reading

Forcing algebras, syzygy bundles, and tight closure (Holger Brenner, survey article)

Some remarks on the affineness of ${}{\mathbb {A} }^{1}$-bundles (Holger Brenner, survey article)

A guide to closure operations in commutative algebra (Neil Epstein, survey article)

The theory of tight closure from the viewpoint of vector bundles (Holger Brenner, Habilitationsschrift)

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)

John Baez explains the use of torsors in physics

Problem list