Last Updated
：2025/11/29
Zariski-Riemann space
Noun
Japanese Meaning
（代数幾何学）ある体Kの部分環kに対して、点がkを含みかつKに含まれる評価環に対応する局所環付き空間。これは複素曲線のリーマン面を一般化した概念である。
（ plural ）
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(algebraic geometry) A locally ringed space of a subring k of a field K, whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.
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Zariski-Riemann space
The Zariski-Riemann space provides a powerful framework for studying birational properties of algebraic varieties by encoding all valuation rings of a function field that contain a given base ring.
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The Zariski-Riemann space provides a powerful framework for studying birational properties of algebraic varieties by encoding all valuation rings of a function field that contain a given base ring.
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