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Preprint Number 1002

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1002. Sylvy Anscombe and Arno Fehm
Characterizing diophantine henselian valuation rings and valuation ideals

Submission date: 3 February 2016.


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.

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