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In this work we show that the classical subject of general valuation theoryand Zariski-Riemann varieties has a much wider scope than commutative algebraand desingularization theory. We construct and investigate birationalprojective limit objects appropriate for the study of countably many birationalmodels at one time. We use nonseparated Riemann varieties to investigate thebirational structure of integral preschemes satisfying the existence conditionof the valuative criterion of properness.

Valuation Theory, Riemann Varieties and the Structure of integral Preschemes