# Differential varieties with only algebraic images

## Rahim Moosa

### University of Waterloo

Consider the following condition on a finite-dimensional differential-algebraic variety *X*: whenever *X→Y* is a dominant morphism, and dim(*Y*) < dim(*X*), then *Y* is (a finite cover of) an algebraic variety in the constants. This property is a specialisation to differentially closed fields of a model-theoretic condition that itself arose as an abstraction from complex analytic geometry. Non-algebraic examples can be found among differential algebraic subgroups of simple abelian varieties. I will give a characterisation of this property that involves differential analogues of “algebraic reduction” and “descent”. This is joint work with Anand Pillay.

Rahim Moosa received his doctorate in 2001 from the University of Illinois at Urbana-Champaign, with Anand Pillay as his advisor. After a series of postdoctoral positions, he joined the faculty at the University of Waterloo, where he is now Associate Professor. He studies model theory, especially in relation to differential algebra, fields, and number theory.