Abelian birational sections

Abstract. Let X be an irreducible variety over a number field K. The birational section conjecture predicts that X admits a rational point if and only if the natural map from the absolute Galois group of K(X) to the absolute Galois group of K admits a continuous section. An abelian variant of this conjecture can be proved when X is a curve whose Jacobian has a finite Tate-Shafarevich group. I will also discuss the case of higher-dimensional varieties.

This is joint work with Hélène Esnault.