Defining coarsenings of valuations

Author: 

Jahnke, F
Koenigsmann, J

Publication Date: 

10 January 2017

Journal: 

Proceedings of the Edinburgh Mathematical Society

Last Updated: 

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

Issue: 

3

Volume: 

60

DOI: 

10.1017/S0013091516000341

page: 

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.

Symplectic id: 

505668

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article