Defining Coarsenings of Valuations
2017 ◽
Vol 60
(3)
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pp. 665-687
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AbstractWe 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.
2019 ◽
Vol 56
(3)
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pp. 918-936
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2012 ◽
Vol 45
(1)
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pp. 113-120
2019 ◽
Vol 125
(1)
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pp. 10008
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2010 ◽
Vol 108
(10)
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pp. 323-329
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