This is joint work with Özlem Beyarslan. In our previous work (published as "Model theory of fields with virtually free group actions", Proc. London Math. Soc., (2) 118 (2019), 221-256; see also preprint), we used an erroneous argument in the proof of Theorem 3.6 saying that if \(G\) is a finitely generated virtually free group, then the theory of \(G\)-actions on fields has a model companion. In our recent paper (to appear in Bull. London Math. Soc.), we show a "strong negation" of the statement from Theorem 3.6 above, that is, we show that if \(G\) is an infinite finitely generated virtually free group, then the theory of \(G\)-actions on fields has a model companion if and only if \(G\) is free. In this talk, I will present some results and conjectures regarding the companionability of the theory of group actions on fields and (time permitting) discuss some related proofs.
Galois actions of finitely generated groups rarely have model companions
14.12.2023 15:00 - 15:50
Organiser:
KGRC
Location: