Valuation Semigroups of Two Dimensional Local Rings
Commutative Algebra
2014-04-30 v2
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.
Cite
@article{arxiv.1105.1448,
title = {Valuation Semigroups of Two Dimensional Local Rings},
author = {Steven Dale Cutkosky and Pham An Vinh},
journal= {arXiv preprint arXiv:1105.1448},
year = {2014}
}
Comments
34 pages. Final version