# MAA

## Seminar

### E.c. Hasse fields - geometric axioms

Seminar Room 1, Newton Institute

#### Abstract

Ziegler proved that the theory of fields with e commuting Hasse derivations has a model companion. This model companion eliminates quantifiers and is an expansion of the theory of separably closed fields of inseparable degree e. I wanted to find an axiomatization of this theory which gives criteria whether a system of Hasse-differential equations and inequalities is solvable (e.g. X'=X and X\neq 0 is not solvable). Such axioms are given in terms of higher prolongation spaces (related to arc spaces). I also found axioms of the theories of e.c. fields with truncated Hasse derivations. This theories are higher order analogues of Wood's DCF-p theories.

**Related Links**

- http://www.math.uni.wroc.pl/~pkowa/ - my web page