D-varieties and the Dixmier-Moeglin Equivalence
By Rahim Moosa
About four years ago, a new application of the model theory of differentially closed fields arose. The target was the Dixmier-Moeglin equivalence problem (DME) in noncommutative affine algebras, as well as a variant for commutative Poisson algebras. It has become clear that the structure of D-varieties (i. e. , finite-dimensional types in DCF), and D-groups, can be used to both prove the DME and produce counterexamples in various settings. There have been a handful of papers exploring and exploiting this connection. I will give an overview of this body of work.