  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.
