Model theory of differential fields in positive characteristic

Omar Leon Sanchez, University of Manchester

While the model theory of differential fields in characteristic zero has been vastly studied since the late 60s, its positive characteristic counterpart has received little attention (or rather exploration). As far as I am aware, the only work on this direction appears in a series of papers of Carol Wood from the early 70's, where she investigates the class of differentially closed fields in characteristic p>0. This theory DCF_p is complete and stable; and one can think of it as the differential analogue of ACF_p. The question that I will address in this talk is: what is the differential analogue of the theory of separably closed fields SCF_p? Somewhat surprisingly, to my knowledge, this has not been dealt with elsewhere. This is joint work with Kai Ino.

MC 5403