Number Theory Seminar

A variety $V$ over a number field $K$ is {\bf Diophantine stable for the extension $L/K$} if the set of $K$-rational points of $V$ is {\it equal} to the set of its $L$-rational points. Following my Alaoglu Memorial Lecture {\it ``Relatively few rational points"} I will discuss recent joint work with Karl Rubin: theorems regarding Diophantine stability, and computations related to a `heuristic' that lead to some striking guesses about it.