Special Colloquium
Jennifer Balakrishnan
Boston University
Rational points on curves and iterated p-adic integrals
Abstract: Let C be a smooth projective curve defined over the rational numbers
with genus at least 2. It was conjectured by Mordell and proved by
Faltings that C has finitely many rational points. However, Faltings'
proof does not give an algorithm for finding these points, and in
practice, given a curve, provably finding its set of rational points
can be quite difficult.
In the case when the Mordell-Weil rank of the Jacobian of C is less
than the genus, the Chabauty-Coleman method can be used to find
rational points, using the construction of certain p-adic line
integrals. Nevertheless, the situation in higher rank is still rather
mysterious. I will discuss some new techniques that apply in the case
when the rank is equal to the genus.
Tuesday November 29, 2016 at 3:00 PM in SEO 636