摘要翻译：
在$\mathbf{C}$上局部有限型代数空间是可分析的当且仅当它是局部分离的，这是现在的一个经典结果。本文研究代数空间的非阿基米德分析。构造了任意对角为闭浸没的非阿基米德解析等价关系的商，并推导出任意非阿基米德域$k$上的有限型局部分离代数空间在刚性空间范畴和$k$上的解析空间范畴中都是可解析的。另外，尽管局部分离性仍然是这两个范畴中可解析性的必要条件，但我们给出了许多令人惊讶的例子，它们在$k$上是不可解析的局部分离光滑代数空间，甚至可以定义在素域上。
---
英文标题：
《Non-archimedean analytification of algebraic spaces》
---
作者：
Brian Conrad, Michael Temkin
---
最新提交年份：
2007
---
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：
  It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct a quotient for any etale non-archimedean analytic equivalence relation whose diagonal is a closed immersion, and deduce that any separated algebraic space locally of finite type over any non-archimedean field $k$ is analytifiable in both the category of rigid spaces and the category of analytic spaces over $k$. Also, though local separatedness remains a necessary condition for analytifiability in either of these categories, we present many surprising examples of non-analytifiable locally separated smooth algebraic spaces over $k$ that can even be defined over the prime field.
---
PDF链接：
https://arxiv.org/pdf/0706.3441