Affine schemes and topological closures in the Zariski-Riemann space of valuation rings

2014/09/17 by Olberding, Bruce
#13A18 #13B22 #13F05 #14A15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.5113

Abstract

Let F be a field, let D be a subring of F, and let \mathfrakX be the Zariski-Riemann space of valuation rings containing D and having quotient field F. We consider the Zariski, inverse and patch topologies on \mathfrakX when viewed as a projective limit of projective integral schemes having function field contained in F, and we characterize the locally ringed subspaces of \mathfrakX that are affine schemes.

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