The study of an algebraically closed field K with a distinguished algebraically closed field L goes back to Keisler’s work in 1964, where he proves a completeness result. Since then there had been many developments around such pairs and more general kinds of pairs of stable structures.

In this talk, we equip each K^n with a topology refining Zariski topology in a way that sets definable in the pair (K,L) are precisely the constructible sets of this topology.

We shall also mention the relations of this topology with Morley rank and another notion of dimension arising from a pregeometry.

URL:https://www.imj-prg.fr/spip.php?article219 END:VEVENT END:VCALENDAR