论文标题
复合物的派生项目化
Derived projectivizations of complexes
论文作者
论文摘要
在本文中，我们研究了Grothendieck在派生的代数几何形状的背景下的Projectivation构造的对应物。我们的主要结果如下：首先，我们定义了结缔分裂复合物的衍生项目化，研究其基本属性，例如有限性能和功能行为，并提供了对其相对复合物的明确描述，然后我们专注于$ [0,1] $ $ $ [0,1] $的相对复合物的衍生项目衍生物。在这种情况下，我们证明了一个广义的Serre定理，这是Beilinson关系的派生版本，并为其派生类别建立半指分解。最后，我们表明许多模量问题适合派生的项目化框架，例如Hecke对应关系中出现的模量空间。我们将结果应用于这些情况。
In this paper, we study the counterpart of Grothendieck's projectivization construction in the context of derived algebraic geometry. Our main results are as follows: First, we define the derived projectivization of a connective complex, study its fundamental properties such as finiteness properties and functorial behaviors, and provide explicit descriptions of their relative cotangent complexes, We then focus on the derived projectivizations of complexes of perfect-amplitude contained in $[0,1]$. In this case, we prove a generalized Serre's theorem, a derived version of Beilinson's relations, and establish semiorthogonal decompositions for their derived categories. Finally, we show that many moduli problems fit into the framework of derived projectivizations, such as moduli spaces that arise in Hecke correspondences. We apply our results to these situations.
