Generic cohomology of function fields and birational anabelian geometry.

In this talk, I will discuss the so-called generic cohomology of a function field, which can be constructed using any suitable cohomology theory. While this object resembles Galois cohomology in many ways, there are subtle but important differences that give this object a more refined structure. I will focus primary on a new birational anabelian result which uses the Hodge-theoretic avatar of generic cohomology.