标题： 诺特概形上的凝聚层的替代模型 显示英文标题

标题： An Alternative Model for Coherent Sheaves over Noetherian Schemes

摘要： 诺特概形上的凝聚层范畴对于研究给定概形的性质非常重要。 对于诺特概形来说，一个众所周知的事实是，其拓扑可以完全从其点的偏序集以及专门化偏序中恢复出来。 在这里，我们证明对于诺特概形上的凝聚层范畴也成立，即： 这个范畴存在一种等价描述，用这个偏序集的“语言”来表达。 首先我们构建结构层的等价概念，然后引入从凝聚层范畴到它上面的某个预层范畴的期望函子，证明这个函子是满忠实的，描述它的本质像，从而找到一个与诺特概形上的凝聚层范畴等价的范畴。 本文基于作者的硕士论文。 显示英文摘要

摘要： The category of coherent sheaves over a noetherian scheme is very important for studying the properties of a given scheme. For noetherian schemes it is a well-known fact that the topology can be fully recovered from the corresponding partially ordered set of its points together with the specializaion partial order. Here we show that the same thing holds for the category of coherent sheaves over a noetherian scheme, i.e. there exists an equivalent description of this category in the "language" of this poset. First we build the equivalent notion of the structure sheaf, then we introduce the desired functor from the category of coherent sheaves to a certain category of presheaves over it, show this functor is fully faithful, describe its essential image and hence find an equivalent category for the category of coherent sheaves over a noetherian scheme. This paper is based on the author's master's thesis.