论文标题
虚拟Riemann-Roch定理几乎是完美的阻塞理论
Virtual Riemann-Roch Theorems for Almost Perfect Obstruction Theories
论文作者
论文摘要
这是一系列作品中的第三件作品，该作品致力于构建虚拟结构滑轮和$ k $ - 模仿理论中的理论不变。研究的中心对象几乎是Y.-H的完美障碍理论。 Kiem和作者是适当的概念，以定义$ k $的不变性 - 许多感兴趣的Moduli堆栈，包括广义的$ K $ - 理论 - 理论上的Donaldson-Thomas不变式。 在本文中，我们在非等价案例和均衡案例（包括COSECTION局部版本）中，在几乎完美的阻塞理论中证明了虚拟的Riemann-Roch定理。这些从Fantechi-Göttsche和Ravi-Sreedhar的虚拟Riemann-Roch定理中概括并删除了技术假设。主要的技术成分是对捆绑堆叠的$ k $ $ k $理论和吉林斯的吉辛地图的处理，以及虚拟TODD类的公式。
This is the third in a series of works devoted to constructing virtual structure sheaves and $K$-theoretic invariants in moduli theory. The central objects of study are almost perfect obstruction theories, introduced by Y.-H. Kiem and the author as the appropriate notion in order to define invariants in $K$-theory for many moduli stacks of interest, including generalized $K$-theoretic Donaldson-Thomas invariants. In this paper, we prove virtual Riemann-Roch theorems in the setting of almost perfect obstruction theory in both the non-equivariant and equivariant cases, including cosection localized versions. These generalize and remove technical assumptions from the virtual Riemann-Roch theorems of Fantechi-Göttsche and Ravi-Sreedhar. The main technical ingredients are a treatment of the equivariant $K$-theory and equivariant Gysin map of sheaf stacks and a formula for the virtual Todd class.
