Characterizing diophantine henselian valuation rings and valuation ideals

Sylvy Anscombe; Arno Fehm

doi:10.1112/plms.12042

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arXiv · 1602.01233

Characterizing diophantine henselian valuation rings and valuation ideals

Sylvy Anscombe·Arno Fehm

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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.

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BibTeX RIS

Sylvy Anscombe, Arno Fehm. 2016-02-03. Characterizing diophantine henselian valuation rings and valuation ideals. https://doi.org/10.1112/plms.12042

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