衍生复几何中的GAGA定理

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2019-04-18 DOI:10.1090/JAG/716

Mauro Porta

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引用次数: 11

摘要

在本文中，我们扩展了由Jacob Lurie在2011年引入的衍生复解析几何的基础。我们首先研究分析函子及其性质。特别地，我们证明了对于有限表示X X的导出的局部概复格式，X an→X X^{\mathrm {an}} \到X的正则映射在导出意义上是平坦的。接下来，我们提供了一个关于推导的复解析空间与几何堆栈的比较结果。利用这些结果，并在作者和余乐宇之前的工作的基础上，我们证明了GAGA定理的一个派生版本。作为一个应用，我们证明了一类衍生的复解析模问题的无穷小变形理论是由微分梯度李代数控制的。

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GAGA theorems in derived complex geometry

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.

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.