Submission date: 11 May 2022

Abstract:

We study the existential theory of equicharacteristic henselian valued fields with a distinguished uniformizer. In particular, assuming a weak consequence of resolution of singularities, we obtain an axiomatization of - and therefore an algorithm to decide - the existential theory relative to the existential theory of the residue field. This is both more general and works under weaker resolution hypotheses than the algorithm of Denef and Schoutens, which we also discuss in detail.

Mathematics Subject Classification: 03C60, 12L05, 11D88

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Full text arXiv 2205.05438: pdf, ps.