Parametrizations of subsets of the space of valuations

2023/08/25 by Novacoski, Josnei Antonio, de Souza, Caio Henrique Silva
#13A18 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.13322

Abstract

In this paper we present different ways to parametrize subsets of the space of valuations on K[x] extending a given valuation on K. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here is slightly different than the ones in the literature and we believe that our approach is more accurate.

Related

• Approximation types describing extensions of valuations to rational function fields
• Extensions of a valuation from K to K[x]
• Algebraic structures on valuations, their properties and applications
• Geometric parametrization of valuations on a polynomial ring
• New structures on valuations and applications