Séminaire d'arithmétique à Lyon

# Vector bundles over smooth affine fourfolds

## by Dr Tariq Syed

Europe/Paris
Description

The generalized Serre question asks whether algebraic vector bundles over topologically contractible smooth affine complex varieties are always trivial. The question has been answered in the affirmative in dimensions 1 and 2 and general classification results for vector bundles over threefolds yield a necessary and sufficient criterion in dimension 3. In this talk, I will explain a sufficient criterion for the triviality of all vector bundles over smooth affine complex fourfolds. Assuming a conjecture by Asok-Østvær, this criterion would imply that vector bundles over topologically contractible smooth affine complex fourfolds are trivial.