The Bass-Quillen conjecture and affine representability for vector bundles

par Daniel Marlowe (University of Warwick)

mercredi 15 avr. 2026, 15:40 → 17:00 Europe/Paris

Salle Pierre Grisvard (Institut Henri Poincaré)

The Morel-Voevodsky A¹-homotopy category is a prime setting in which to approach questions in geometry by means of topological techniques. A notable example of this is the importation of obstruction theory into the study of vector bundles over algebraic varieties; this allows one to reduce statements about such vector bundles to cohomological criteria, and in doing so demonstrates that the heart of the matter is often a computation of a K-theoretic nature.

 

In this expository talk, we will review some elements of this motivic obstruction theory, and in particular the key geometric ingredient in the form of Lindel-Popescu's solution to the Bass-Quillen conjecture. We will then sketch its role in the proof of affine representability for vector bundles in the A¹-homotopy category.