Simon Cooper: Introduction to Motives

Abstract:

I will give a very brief introduction to the theory of (pure) motives. The focus will be on the idea that motives should give us a universal cohomology theory, defined over the rationals, for smooth projective varieties. I will outline some properties the category of motives should satisfy in order to achieve this and, if I have time, highlight some important obstacles to proving that existing candidates for the category of pure motives satisfy these properties.