科研之友
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摘要
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 O-definable (non-trivial) Henselian valuations. We then draw some Galois-theoretic conclusions from our results.
- 出版日期2017-8
