Twists of elliptic curves with a large set of integral points over function fields

Algebra Seminar
Monday, April 12, 2010 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 255
Ricardo Conceicao – Oxford College of Emory University –
Douglas Ulmer
We will explicitly construct twists of elliptic curves with an arbitrarily large set of integral points over $\mathbb{F}_q(t)$. As a motivation to our main result, we will discuss a conjecture of Vojta-Lang concerning the behavior of integral points on varieties of log-general type over number fields and present a natural translation to the function field setting. We will use our construction to provide an isotrivial counter-example to this conjecture. We will also show that our main result also provides examples of elliptic curves with arbitrarily large set of independent points and of function fields with large $m$-class rank.