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SUMMARY:Ulla Karhumäki - The Borovik-Cherlin conjecture in ACF
DTSTART:20261001T130000Z
DTEND:20261001T140000Z
DTSTAMP:20261011T222700Z
UID:indico-event-17419@indico.math.cnrs.fr
DESCRIPTION:The Borovik–Cherlin conjecture predicts that the only generi
 cally (n+2)-transitive permutation group (G\,X) of finite Morley rank\, wi
 th RM(X)=n\, is the natural action of PGL_{n+1}(K) on the projective n-spa
 ce P^n(K). It is natural to ask whether the Borovik–Cherlin conjecture h
 olds when (G\,X) is definable in a model of ACF. In characteristic 0\, Pop
 ov obtained a complete classification of highly transitive actions of simp
 le algebraic groups. Building on this\, Freitag and Moosa recently verifie
 d the Borovik–Cherlin conjecture in ACF_0. We remove the characteristic 
 assumption and thus prove that the Borovik–Cherlin conjecture holds in A
 CF.\nThis is joint work with Nick Ramsey.\n\nhttps://indico.math.cnrs.fr/e
 vent/17419/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/17419/
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