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arXiv · 2609.02198

The Borovik-Cherlin conjecture holds in ACF

Ulla Karhumäki·Nicholas Ramsey
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Abstract

We show that every faithful, transitive, and generically $(n+2)$-transitive action of a connected group $G$ on an irreducible variety $X$ of dimension $n > 0$, all defined over an algebraically closed field $F$, is isomorphic to the natural action of the projective linear group $PGL_{n+1}(F)$ on the projective space $\mathbb{P}^n(F)$. More precisely, we establish the Borovik-Cherlin conjecture for permutation groups $(G,X)$ definable in models of $ACF$.

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Ulla Karhumäki, Nicholas Ramsey. 2026-09-02. The Borovik-Cherlin conjecture holds in ACF. https://arxiv.org/abs/2609.02198

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