The supersimple field conjecture

A supersimple field is a field whose theory is supersimple; a field is PAC if every absolutely irreducible variety over it has a rational point, and its absolute Galois group is small if it has only finitely many closed subgroups of each finite index. The supersimple field conjecture. Every infinite supersimple field is perfect PAC with small absolute Galois group. This conjecture predicts the converse to the known result that perfect PAC fields with small absolute Galois group are supersimple; its status is not resolved in the supplied text.