Title: Subfields of ample fields

Abstract: A field K is called ample if every smooth variety V over K
that has a K-rational point has infinitely many of them. It is known
that in this situation the set of K-rational points is even
Zariski-dense in V and has maximal cardinality. I will present a result
that implies that, in addition, V has 'many' K-rational points with
respect to proper subfields of K. I will give several applications of
this, for example to the structure of diophantine subsets of ample
fields. These applications establish a link to recent developments in
valuation theory and the model theory of fields.
(Talk in Hebrew)