%0 Journal Article
%T Valuation Semigroups of Two Dimensional Local Rings
%A Steven Dale Cutkosky
%A Pham An Vinh
%J Mathematics
%D 2011
%I arXiv
%R 10.1112/plms/pdt023
%X 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.
%U http://arxiv.org/abs/1105.1448v2