Oratrices et orateurs et résumés > O'sullivan Peter

One of the main difficulties in the theory of pure motives is that, in the absence of a proof of the standard conjectures, it is not known that the category of motives modulo homological equivalence is abelian. Yves Andre has shown a way to circumvent this difficulty by passing to a category of motives defined using the larger class of motivated cycles instead of algebraic cycles modulo homological equivalence. We describe another approach to the problem, using an analogy between motives and equivariant vector bundles.