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.
By Matthias Aschenbrenner
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By Raf Cluckers
By Arthur Forey
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By Carlos Simpson
By Zsolt Patakfalvi
