2009/05/27 by Steven Dale Cutkosky, Cutkosky, Steven Dale, Samar ElHitti +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.0905.4518
arxiv created 2009/05/27 · openalex publication_date 2009/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that R is a local domain essentially of finite type over a field of characteristic 0, and ν a valuation of the quotient field of R which dominates R. The rank of such a valuation often increases upon extending the valuation to a valuation dominating R, the completion of R. When the rank of ν is 1, Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than 1, there is no natural ideal in R that leads to this obstruction. We extend their result on the resolution of prime ideals of infinite value to valuations of arbitrary rank.