Overrings of two-dimensional Noetherian domains representable by Noetherian spaces of valuation rings

摘要

Let D be a Noetherian domain of Krull dimension 2, and let H subset of R be integrally closed overrings of D. We examine when H can be represented in the form H = (boolean AND V-V is an element of Sigma) boolean AND R, with Sigma a Noetherian subspace of the Zariski-Riemann space of the quotient field of D. We characterize also the special case in which Sigma can be chosen to be a finite character collection of valuation overrings of D. (C) 2007 Elsevier B.V. All rights reserved.