# Algebra Seminar talk

2019-10-31 (Thursday!) 13:15

Jean **Gillibert***Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank*

Abstract:

We introduce the use of p-descent techniques for elliptic surfaces over
a perfect field of characteristic not 2 or 3. Under mild hypotheses, we
obtain an upper bound for the rank of a non-constant elliptic surface.
When p = 2, this bound is an arithmetic refinement of a well-known
geometric bound for the rank deduced from Igusa’s inequality. This
answers a question raised by Ulmer. We are also able to deduce some
heuristics in favor of a conjecture by Silverman on the asymptotic
behavior of the rank. This is joint work with Aaron Levin.