Kurs:Vector bundles and their torsors (Kolkata 2011)

This is a short course given by Holger Brenner at the Indian Statistical Institute in Kolkata in July 2011.

Lecture 1 - Locally free sheaves and vector bundles

Lecture 2 - Torsors and forcing algebras

Lecture 3 - Forcing algebras and closure operations

Lecture 4 - Affineness of torsors

Lecture 5 - Torsors over projective curves

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