James Freitag : Intersections of isogeny classes and varieties

Posted by David E. Marker , part of the Logic Seminar.

At

Oct. 16, 2014, 1 p.m.

In

SEO 636

Abstract

Take $ \alpha \in GL_2$ and a complex number $a$. There are at most $36^7$ complex numbers $b$ such that the elliptic curves $E_a$ and $E_b$ are isogenous and $E_ {\alpha (a)}$ and $E_ {\alpha (b)} $ are isogenous. Proving this fact along with an effective form of a special case of the Zilber-Pink conjecture uses input from model theory, differential algebra, and diophantine geometry. We will describe the proof and partial generalizations to various moduli spaces of abelian varieties.