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摘要翻译：
本文研究了格式态射上的相对Riemann-Zariski空间，推广了域的经典Riemann-Zariski空间。我们证明了与经典RZ空间类似，相关的RZ空间既可以描述为局部环空间范畴中方案的射影极限，也可以描述为一定的赋值空间。我们应用这些空间证明了以下两个新结果：相对曲线稳定修正定理的一个强版本；一个分解定理，它断言拟紧格式和拟分离格式之间的任何分离态射都是仿射态射和真态射的合成。（特别地，我们得到了Nagata紧致定理的一个新的证明。）
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英文标题：
《Relative Riemann-Zariski spaces》
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作者：
Michael Temkin
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)
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PDF链接：
https://arxiv.org/pdf/0804.2843
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