Transitive-module identification conjecture

Let $(G,V)$ be a module of finite Morley rank, with $G$ connected and simple modulo its at most finite centre. Suppose that $G$ is transitive on $V\setminus\{0\}$ and generically $2$-transitive. Transitive-module identification conjecture. The module $(G,V)$ is definably equivalent to $(\operatorname{SL}_n(\mathbb{K}),\mathbb{K}^n)$ for some definable field $\mathbb{K}$. The corresponding result is known in the algebraic category, but the general finite-Morley-rank problem remains open and is viewed as a test case for linearisation methods.