Uniformity of integral points and Lang-Vojta’s conjecture

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, November 8, 2016 - 11:15am to 12:15pm
Location: 
LOM 205
Speaker: 
Kenny Ascher
Speaker affiliation: 
Brown University
Event description: 

Caporaso, Harris, and Mazur proved, assuming Lang’s conjecture, that the number of rational points on a
smooth curve of genus greater than 1 is uniformly bounded by an integer depending solely on the genus and
number field the curve is defined over. This theorem was proven by means of a purely algebro-geometric
theorem known as a fibered power theorem. We discuss how this uniformity result follows from the fibered
power theorem, and discuss recent extensions (joint with A. Turchet) aiming to, assuming the Lang-Vojta
conjecture, study uniformity results for integral points on curves and surfaces of log general type.