Abstract

In this talk, l will first explain how motivic homotopy theory allows to classify vector bundles usinginvariants in certain cohomology groups that are amenable to computations. For smooth complexthreefolds, l wil compare these invariants with the topological ones giving necessary and sufficientconditions for a topological vector bundle to admit an algebraic structure. l will then focus on thecase of schemes over the real numbers, where the situation is more complicated.