Key Polynomials in dimension 2

2019/01/29 by Mahboub, Wael, Spivakovsky, Mark
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.10043

Abstract

Let R be a two-dimensional regular local ring. In this paper, we prove that there is a bijection between the set of all valuations of Quot(R) centered at R and valuations of k(x,y) centered at k[x,y]_(x,y), where k is the residue field of R and x and y are independent variables. Moreover, we give a new proof, for the fact that the set of all normalized real valuations centered at R admits a structure of non metric tree.

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