Valuation Semigroups of Two Dimensional Local Rings

Abstract

We consider the question of when a semigroup is the semigroup of a valuation dominating a two dimensional noetherian local domain, giving some surprising examples. We give a necessary and sufficient condition for the pair of a semigroup S and a field extension L/k to be the semigroup and residue field of a valaution dominating a regular local ring R of dimension two with residue field k, generalizing the theorem of Spivakovsky for the case when there is no residue field extension.

34 pages. Final version

References in corpus (3)

• Valuations in algebraic field extensions
• Extending a valuation centered in a local domain to the formal completion
• Deformation of nonrelativistic space-time and forces noticed by noninertial observer

Cited by in corpus (6)

• The role of defect and splitting in finite generation of extensions of associated graded rings along a valuation
• Multiplicities Associated to Graded Families of Ideals
• Discrete equivalence of non-positive at infinity plane valuations
• Finite Generation of Extensions of Associated Graded Rings Along a Valuation
• Overweight deformations of affine toric varieties and local uniformization
• Generating Sequences and Semigroups of Valuations on 2-Dimensional Normal Local Rings