MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1002

Preprint Number 1002

Previous Next Preprint server


1002. Sylvy Anscombe and Arno Fehm
Characterizing diophantine henselian valuation rings and valuation ideals
E-mail:

Submission date: 3 February 2016.

Abstract:

We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative results on diophantine henselian valuation rings and diophantine valuation ideals in the literature. We also treat questions of uniformity and we apply the results to show that a given field can carry at most one diophantine nontrivial equicharacteristic henselian valuation ring or valuation ideal.

Mathematics Subject Classification: 11U09 (Primary) 03C60, 11D88, 12J10, 14G05, 14G20 (Secondary)

Keywords and phrases:

Full text arXiv 1602.01233: pdf, ps.


Last updated: February 12 2016 17:18 Please send your corrections to: