Connectedness and integrally closed local overrings of two-dimensional regular local rings

2024/06/16 by Heinzer, William, Loper, K. Alan, Olberding, Bruce +1 · 1 citation
#13A18 #13H05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.10966

Abstract

Let D be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of D that dominate D and the integrally closed local overrings of D that are not essential valuation rings or divisorial valuation rings of D.

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