We investigate the question which henselian valued fields are NIP. In equicharacteristic 0, this is well understood due to the work of Delon: an henselian valued field of equicharacteristic 0 is NIP (as a valued field) if and only if its residue field is NIP (as a pure field). For perfect fields of equicharacteristic p, a characterization can be obtained by combining the work of Bélair and Kaplan-Scanlon-Wagner. In this talk, I will present a characterization for henselian fields (K, v) to be NIP as long as the residue fields of all coarsenings of v have finite degree of imperfection. In particular, we will construct examples of NIP henselian fields with imperfect residue fields. This is joint work with Sylvy Anscombe.
De Matthias Aschenbrenner
De Antoine Chambert-Loir
De Matthew Morrow
De Ehud Hrushovski
De Raf Cluckers
De Bernard Teissier
