Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Nov 13, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Jason Starr
Stony Brook University
Title |
Rational points of varieties over global function fields |
Abstract |
This is joint work with Chenyang Xu. Combining work of Esnault with work of de Jong - He - Starr on “rational simple connectedness”, we prove the existence of rational points of many varieties defined over global function fields, i.e., function fields of curves over finite fields. In this way we get uniform proofs and extensions of (1) Lang’s theorem that every global function field $K$ is $C_2$, (2) a theorem of Brauer - Hasse - Noether that the period equals the index for every division algebra over $K$, and (3) the “split case” of Harder’s proof of Serre’s Conjecture II over $K$. We also get upper bounds on the heights of our rational points, independent of the characteristic. |
Algebraic Geometry