Valuation Semigroups of Two Dimensional Local Rings

Details Valuation Semigroups of Two Dimensional Local Rings Valuation Semigroups of Two Dimensional Local Rings

2011-05-07

arxiv.org/abs/1105.1448v1

Mathematics

Commutative Algebra

34 pages

Scientific paper

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.

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