Ulla Karhumäki - The Borovik-Cherlin conjecture in ACF

jeudi 1 oct. 2026, 15:00 → 16:00 Europe/Paris

112 (ICJ)

The Borovik–Cherlin conjecture predicts that the only generically (n+2)-transitive permutation group (G,X) of finite Morley rank, with RM(X)=n, is the natural action of PGL_{n+1}(K) on the projective n-space P^n(K). It is natural to ask whether the Borovik–Cherlin conjecture holds when (G,X) is definable in a model of ACF. In characteristic 0, Popov obtained a complete classification of highly transitive actions of simple algebraic groups. Building on this, Freitag and Moosa recently verified the Borovik–Cherlin conjecture in ACF_0. We remove the characteristic assumption and thus prove that the Borovik–Cherlin conjecture holds in ACF.

This is joint work with Nick Ramsey.