Of limit key polynomials
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Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane-Vaquié key polynomials for valuations μ ≤ν and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if char(K) = 0 we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.
CitationAlberich, M. [et al.]. Of limit key polynomials. "Illinois journal of mathematics", 1 Abril 2021, vol. 65, núm. 1, p. 201-229.