Computation of residual polynomial operators of inductive valuations

2019/01/15 by de Oliveira, Nathália Moraes, Nart, Enric
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.04937

Abstract

Let (K,v) be a valued field, and μ an inductive valuation on K[x] extending v. Let G_μ be the graded algebra of μ over K[x], and κ the maximal subfield of the subring of G_μ formed by the homogeneous elements of degree zero. In this paper, we find an algorithm to compute the field κ and the residual polynomial operator R_μ: K[x]→κ[y], where y is another indeterminate, without any need to perform computations in the graded algebra. This leads to an OM algorithm to compute the factorization of separable defectless polynomials over henselian fields.

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