Submission date: 19 January 2015.

Abstract:

We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax-Kochen-Ershov principle, which roughly says that the existential theory of an equicharacteristic henselian valued field (of arbitrary characteristic) is determined by the existential theory of the residue field; in particular, it is independent of the value group. As an immediate corollary, we get an unconditional proof of the decidability of the existential theory of F_q((t)).

Mathematics Subject Classification: 03C60, 12L12, 12J10, 11U05, 12L05

Keywords and phrases:

Full text arXiv 1501.04522: pdf, ps.