Title: Solvable points on genus one curves

Abstract:
A genus one curve defined over Q which is locally trivial may not have a rational point. It is natural to study the classes of field extensions over which all such curves obtain a global point. I will explain how we have shown that every locally trivial genus one curve with semistable Jacobian has a point defined over a solvable extension of Q. This is joint work with A. Wiles.