A theorem of Lichtenbaum states, that every proper, regular curve C over a discrete valuation domain R is projective. This theorem is generalized to the case of an arbitrary valuation domain R using the following notion of regularity for non-noetherian rings introduced by Bertin: the local ring O-C,O-x of a point x is an element of C is called regular, if every finitely generated ideal I has finite projective dimension. The generalization is a particular case of a projectivity criterion for proper, normal R-curves: such a curve C is projective if for every irreducible component Y of its closed fiber C-m there exists a closed point P of the generic fiber of C such that the Zariski closure (P) over bar meets Y and meets C-m in regular points only.
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