GAGA theorems in derived complex geometry
GAGA theorems in derived complex geometry
复制标题
导出复杂几何中的 GAGA 定理
DOI：
--
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
Mauro Porta
中科院分区：
文献类型：
--
作者：
Mauro Porta
在本文中，我们扩展了Jacob Lurie在2011年引入的导出复解析几何的基础。我们首先研究分析函子及其性质。特别地，我们证明了对于一个导出的复格式，
X
X
正则映射
X
一
n
→
X
X^{\mathrm {an}} \to X
在派生意义上是平的。接下来，我们提供了一个比较结果，导出复解析空间的几何堆栈。利用这些结果并在作者和Tony Yue Yu以前工作的基础上，我们证明了GAGA定理的一个导出版本。作为应用，我们证明了导出的复解析模问题的无穷小形变理论是由微分分次李代数所支配的。
In this paper, we expand the foundations of derived complex analytic geometry introduced by Jacob Lurie in 2011. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme locally almost of finite presentation
X
X
, the canonical map
X
a
n
→
X
X^{\mathrm {an}} \to X
is flat in the derived sense. Next, we provide a comparison result relating derived complex analytic spaces to geometric stacks. Using these results and building on the previous work of the author and Tony Yue Yu, we prove a derived version of the GAGA theorems. As an application, we prove that the infinitesimal deformation theory of a derived complex analytic moduli problem is governed by a differential graded Lie algebra.
全球衍生周期图
影响因子：
1.7
作者：
Di Natale C
通讯作者：
Di Natale C