# Defining coarsenings of valuations

Jahnke, F
Koenigsmann, J

10 January 2017

## Journal:

Proceedings of the Edinburgh Mathematical Society

## Last Updated:

2020-08-02T19:23:35.37+01:00

3

60

## DOI:

10.1017/S0013091516000341

665-687

## abstract:

We study the question of which Henselian fields admit definable Henselian valuations (with or without parameters). We show that every field that admits a Henselian valuation with non-divisible value group admits a parameter-definable (non-trivial) Henselian valuation. In equicharacteristic 0, we give a complete characterization of Henselian fields admitting a parameter-definable (non-trivial) Henselian valuation. We also obtain partial characterization results of fields admitting-definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results.

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