Tom Weston,
An introduction to etale cohomology
Abstract: Etale cohomology, invented by Grothendieck and Artin in the
1960's, is a purely algebraic replacement for singular cohomology of
complex manifolds. In this talk I will try to emphasize the more concrete
aspects of the theory, rather than obsessing over the foundations. In
particular, I will explain the computation of the etale cohomology of
curves over algebraically closed fields. I will then go on to discuss the
interconnections between the theory over finite fields and over the
complex numbers.