摘要翻译:
本文首先在环空间上引入仿射结构的概念,然后得到仿射结构的几个性质。环空间上的仿射结构主要来源于数域上的代数格式的复解析空间,其行为类似于光滑流形上的微分结构。正如人们对微分流形所做的那样,我们将使用仿射变换的伪群来定义环空间上的仿射图谱。如果空间上的图谱是最大的,则称其为仿射结构。仿射结构是允许的,如果在下空间上存在一个束,使得它们在所有仿射图上重合,这些仿射图实际上是一个方案的仿射开集。严格地将一个格式定义为具有特定仿射结构的环空间,如果仿射结构在某些特殊情况下起作用,如代数格式的解析空间。特别地,通过空间上仿射结构的整体,我们将分别得到两个空间同胚和两个格式同构的充要条件,这是本文的两个主要定理。因此,空间和方案上的仿射结构的整体作为局部数据,分别编码和反映了空间和方案的全局性质。
---
英文标题:
《Affine Structures on a Ringed Space and Schemes》
---
作者:
Feng-Wen An
---
最新提交年份:
2010
---
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
--
---
英文摘要:
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number fields, behave like differential structures on a smooth manifold. As one does for differential manifolds, we will use pseudogroups of affine transformations to define affine atlases on a ringed space. An atlas on a space is said to be an affine structure if it is maximal. An affine structure is admissible if there is a sheaf on the underlying space such that they are coincide on all affine charts, which are in deed affine open sets of a scheme. In a rigour manner, a scheme is defined to be a ringed space with a specified affine structure if the affine structures are in action in some special cases such as analytical spaces of algebraic schemes. Particularly, by the whole of affine structures on a space, we will obtain respectively necessary and sufficient conditions that two spaces are homeomorphic and that two schemes are isomorphic, which are the two main theorems of the paper. It follows that the whole of affine structures on a space and a scheme, as local data, encode and reflect the global properties of the space and the scheme, respectively.
---
PDF链接:
https://arxiv.org/pdf/0706.0579