Let ν be a valuation of arbitrary rank on the polynomial ring with coefficients in a field K. We prove comparison theorems between MacLane–Vaquié key polynomials for valuations and abstract key polynomials for ν. Also, some results on invariants associated to limit key polynomials are obtained. In particular, if , we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.
"Of limit key polynomials." Illinois J. Math. 65 (1) 201 - 229, April 2021. https://doi.org/10.1215/00192082-8827671