March 29
Martin Hils,
University of Münster
Geometric model theory in separably closed valued fields
This talk is a sequel to my talk in the Kolchin seminar. Let $p$ be a prime number and $e\geq 1$ a fixed natural number. We will consider the theory of separably closed non-trivially valued fields of characteristic $p$ and degree of imperfection $e$, either in a language where a $p$-basis is named or with $e$ commuting stacks of Hasse derivations. Denote the latter by $SCVH_{p,e}$.
We will first sketch a proof of the classification of imaginaries in $SCVH_{p,e}$ by the geometric sorts of Haskell-Hrushovski-Macpherson, using prolongations. We will then explain how these may be used to reduce more phenomena of geometric model theory in $SCVH_{p,e}$ to the algebraically closed case, e.g., a description of the stable part and the stably dominated types, yielding metastastability of $SCVH_{p,e}$. This is joint work with Moshe Kamensky and Silvain Rideau.