Abstract
Let D be a 2-dimensional regular local ring and let Q(D) denote the quadratic tree of 2-dimensional regular local overrings of D. We explore the topology of the tree Q(D) and the family R(D) of rings obtained as intersections of rings in Q(D). If A is a finite intersection of rings in Q(D), then A is Noetherian and the structure of A is well understood. However, other rings in R(D) need not be Noetherian. The two main goals of this paper are to examine topological properties of the quadratic tree Q(D), and to examine the structure of rings in the set R(D).
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