6 problems

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…

Let $(G,V)$ be a faithful, irreducible module of finite Morley rank, where $G=\mathbb{G}(\mathbb{K})$ is the group of $\mathbb{K}$-points of a simple algebraic group. Definable twi…

Let $(G,V)$ be a faithful, irreducible module of finite Morley rank, with $G$ connected. A pseudoreflection subgroup is an abelian subgroup $R$ such that … and $R$ acts transitivel…

Let $(G,V)$ be a faithful module of finite Morley rank, and suppose that $V$ has Morley rank $n$ and $G$ is generically $n$-transitive. Highly generically transitive module conject…

Finite generation conjecture. For every $c13\zeta\in S$, the set $c13\mathscr{M}_{\zeta}$ is finitely generated as a $c13\mathbb{Z}[\zeta,\zeta^{-1}]$-module. More generally,

Generator-and-relation conjecture. The following $\g^a$-module M_\bm is isomorphic to