Holly Krieger : Uniform boundedness of S-units in the images of rational maps

Posted by Abel Castillo , part of the Graduate Number Theory Seminar.

At

Nov. 6, 2012, 3 p.m.

In

SEO 512

Abstract

I will discuss joint work with A. Levin, Z. Scherr, and T. Tucker, proving some cases of a conjecture of A. Levin on the uniform boundedness of the number of S-units in images of rational maps defined over number fields, utilizing results of Evertse et al on linear unit equations. I will also discuss the conjecture as a consequence of the famous conjecture of Caporaso, Harris, and Mazur on the uniformity of the number of rational points on curves of fixed genus over a fixed number field.