Invariants of limit key polynomials

Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández, Jordi Guàrdia, Enric Nart, Joaquim Roé

Published 2020-05-09Version 1

Let $\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaqui\'e key polynomials for valuations $\mu\le\nu$ and abstract key polynomials for $\nu$. Also, some results on invariants attached to limit key polynomials are obtained. In particular, if $\operatorname{char}(K)=0$ we show that all limit key polynomials of unbounded continuous MacLane chains have numerical character equal to one.