标题： 将拟凝聚理想层视为环的理想 显示英文标题

标题： Viewing Quasi-Coherent Sheaves of Ideals as Ideals of a Ring

摘要： 本文提出了一种将给定爆破的拟凝聚理想层视为环的正则理想的技术。在本文中，我们首先描述(Zariski)模型为相对于整数域$D$的分离且有限型的整数概形。我们然后通过相交Nagata函数环，为给定的射影模型（例如$D$上有限生成理想的爆破）构造一个环$D^*$。$D^*$的谱包含射影模型，但类似于Proj构造，它还包括额外的素理想。我们表征了相关的理想，并从$D^*$的谱构造了一个到模型的忠实平坦态射。最后，使用Abhyankar关于模型上理想定义，我们将$D^*$的相关理想与相应射影模型的拟凝聚理想层进行识别。 显示英文摘要

摘要： This paper presents a technique for viewing quasi-coherent sheaves of ideals of a given blowup as regular ideals of a ring. In the paper, we first describe (Zariski) models as integral schemes that are separated and of finite type over an integral domain $D$. We then construct a ring $D^*$ for a given projective model (e.g. blowup of $D$ over a finitely generated ideal) by intersecting Nagata function rings. The spectrum of $D^*$ contains the projective model, but similar to the Proj-construction, it includes additional prime ideals. We characterize the relevant ideals and construct a faithfully flat morphism of schemes from the spectrum of $D^*$ to the model. Finally, using Abhyankar's definition of ideals on models, we identify the relevant ideals of $D^*$ with the quasi-coherent sheaves of ideals of the corresponding projective model.