Georgia Institute of Technology College of Sciences

Algebraic geometry has a plethora of cohomology theories, including the derived functor, de Rham, Cech, Galois, and étale cohomologies. We will give a brief overview of some of these theories and explain how they are unified by the theory of motives. A motive is constructed to be a “universal object” through which all cohomology theories factor. We will motivate the theory using the more familiar examples of Jacobians of curves and Eilenberg-Maclane spaces, and describe how motives generalize these constructions to give categories which encode all the cohomology of various algebro-geometric objects. The emphasis of this talk will be on the motivation and intuition behind these objects, rather than on formal constructions.