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On Kaplansky's embedding theorem
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DOI：10.4064/ap241028-7-9.png)
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Abstract
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Let R be a complete equicharacteristic noetherian local domain with an algebraically closed residue field k. Let nu be a zero-dimensional valuation centered in R with value group Phi. We prove that if the value semigroup Gamma = nu(R \ {0}) of the valuation is finitely generated or the valuation is of rank 1, the valuation nu is the restriction, via an embedding R subset of k[[t Phi >= 0]], of the t-adic valuation nu t of the ring of Hahn series with coefficients in k and exponents in Phi >= 0. This embedding is given by the series
Keywords:
valuations
local uniformization
Kaplansky embedding
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0.3
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24
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