Abstract
Separably closed fields are stable. When they are not algebraically closed, they are rather complicated from a model theoretic point of view: they are not super-stable, they admit no non trivial continuous rank and they have the dimensional order property. But they have a fairly good theory of types and independence, and interesting minimal types. Hrushovski used separably closed fields in his proof of the Mordell-Lang Conjecture for function fields in positive characteristic in the same way he used differentially closed fields in characteristic zero ([Hr 96], see [Bous] in this volume). In particular he proved that a certain class of minimal types, which he called thin, are Zariski geometries in the sense of [Mar] section 5. He then applied to these types the strong trichotomy theorem valid in Zariski geometries.
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Delon, F. (1998). Separably closed fields. In: Bouscaren, E. (eds) Model Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68521-0_9
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DOI: https://doi.org/10.1007/978-3-540-68521-0_9
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