论文标题
代数叶子和衍生的几何学II：Grothendieck-Riemann-Roch定理
Algebraic foliations and derived geometry II: the Grothendieck-Riemann-Roch theorem
论文作者
论文摘要
这是基于衍生叶子的中心概念的衍生代数几何形状的叶子研究的第二篇论文。我们引入了用于衍生叶的干式系数，称为准晶晶体，并沿给定衍生的叶片构建了一定的差异算子的DG - 代数，其特性可以将准连续性晶体解释为差异算子的模块。我们使用这种解释来介绍准连晶晶体上良好过滤的概念，并定义特征周期的概念。最后，我们证明了一个表达特征周期的形成的Grothendieck-Riemann-Roch（GRR）公式与沿正确和准平滑的形态兼容。从中推导了几个示例和应用，例如在可能的单数方案上的D模块的GRR公式，以及弱弗雷姆运算符的叶状索引公式。
This is the second of series of papers on the study of foliations in the setting of derived algebraic geometry based on the central notion of derived foliation. We introduce sheaf-like coefficients for derived foliations, called quasi-coherent crystals, and construct a certain sheaf of dg-algebras of differential operators along a given derived foliation, with the property that quasi-coherent crystals can be interpreted as modules over this sheaf of differential operators. We use this interpretation in order to introduce the notion of good filtrations on quasi-coherent crystals, and define the notion of characteristic cycle. Finally, we prove a Grothendieck-Riemann-Roch (GRR) formula expressing that formation of characteristic cycles is compatible with push-forwards along proper and quasi-smooth morphisms. Several examples and applications are deduced from this, e.g. a GRR formula for D-modules on possibly singular schemes, and a foliated index formula for weakly Fredholm operators.
