Jim Freitag : The Frobenius for Almost Every p

Posted by Holly Krieger , part of the Graduate Number Theory Seminar.

At

Sept. 15, 2010, 3 p.m.

In

SEO 427

Abstract

Hrushovski proved that the theory of the q-Frobenius (for q a power of p) acting on an algebraically closed field of characteristic p for almost every prime is ACFA (a theory studied by model theorists). We talk about some general constructions from algebra (like ultraproducts). Then, we will investigate some simple geometry of structures obeying the axioms of ACFA. Specifically, we might give geometric proofs of things like: (1) every difference variety of transformal transcendence degree m is birational to a difference variety in $ \mathbb{A}^{m+1} $ and is isomorphic to a (almost) difference variety in $ \mathbb{P}^{2m+1} $ or (2) transformal transcendence degree is definable in families.