Number Theory Seminar
Henri Gillet
UIC
A (very) special case of Bombieri-Lang for varieties over a function field of characteristic $p$.
Abstract: The function field analog of the Bombieri-Lang conjecture asserts that if $X$ is a smooth projective variety over a
function field $K/k$, and $X$ is of general type, then if $X(K)$ is dense in $X$, then $X$ is isotrivial
(defined over the ground field $k$, roughly speaking). Grauert proved this for curves in characteristic zero, and
Samuel extended Grauert's result to characteristic $p>0$ (these are the function field analogs of the Mordell conjecture).
Noguchi, and independently Martin-Deschamps extended Grauert's argument to the case where $X$ is of arbitrary dimension
with ample cotangent sheaf. I will discuss to what extent one can adapt the arguments of
Noguchi, Martin-Deschamps, and Samuel to varieties in positive characteristic.
Tuesday November 20, 2012 at 3:00 PM in SEO 636