Event Detail

Morley rank is a model-theoretic notion of dimension generalizing Zariski dimension from algebraic geometry. Here, we discuss a three-dimensional “geometry of involutions’’ arising in certain groups of finite Morley rank (fMr) that possess a subgroup C whose conjugates (1) generically cover the group and (2) intersect trivially. The resulting geometry is that of a generically defined projective 3-space, and our focus is on whether it is genuine or not: a distinction that separates SO3(ℝ) (which is not of fMr) from PGL2(ℂ) (which is). Our main result identifies a condition on the subgroup Cthat, if violated, implies that the geometry is genuine and the group does not exist (as it cannot have fMr). As an application of this result, we unify and generalize several known results about the elimination of involutions from certain non-algebraic (but possibly existent and possibly “definably linear’’) groups of fMr.

This is joint work with Adrien Deloro.