Motives and motivic cohomology

Student Algebraic Geometry Seminar
Friday, February 16, 2018 - 10:10
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
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.