TY - JOUR
T1 - Of limit key polynomials
AU - Alberich-Carramiñana, Maria
AU - Boix, Alberto F.F.
AU - Fernández, Julio
AU - Guàrdia, Jordi
AU - Nart, Enric
AU - Roé, Joaquim
N1 - Publisher Copyright:
© 2021 by the University of Illinois at Urbana–Champaign.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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/ D 0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.
AB - 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/ D 0, we show that all the limit key polynomials of unbounded continuous families of augmentations have the numerical character equal to one.
UR - http://www.scopus.com/inward/record.url?scp=85103603865&partnerID=8YFLogxK
U2 - 10.1215/00192082-8827671
DO - 10.1215/00192082-8827671
M3 - Article
AN - SCOPUS:85103603865
SN - 0019-2082
VL - 65
SP - 201
EP - 229
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1
ER -