论文标题
Riemann-Roch定理在单型2类中
Riemann-Roch theorems in monoidal 2-categories
论文作者
论文摘要
平滑而正确的DG代数具有一个欧拉类，在代数的Hochschild同源性中。这个Euler类值得这个名字，因为它满足了许多熟悉的属性，包括与代数的Hochschild同源性及其相反的熟悉的配对兼容。这种兼容性是Shklyarov和Petit的Riemann-Roch定理。 在本文中，我们证明了这些Riemann-Roch定理的广泛概括。我们从DG-Algebras及其双模型的生物概括到单型生物游戏，从Euler类到非身份图的痕迹。我们的概括还意味着光谱Riemann-Roch定理。 我们将此结果视为二维广义恢复假设的实例化。该观点绘制了与其他许多其他结果相关的结果，这些结果将欧拉特征和类别的结果概括为生物痕迹。
Smooth and proper dg-algebras have an Euler class valued in the Hochschild homology of the algebra. This Euler class is worthy of this name since it satisfies many familiar properties including compatibility with the familiar pairing on the Hochschild homology of the algebra and that of its opposite. This compatibility is the Riemann-Roch theorems of Shklyarov and Petit. In this paper we prove a broad generalization of these Riemann-Roch theorems. We generalize from the bicategory of dg-algebras and their bimodules to monoidal bicategories and from Euler class to traces of non identity maps. Our generalization also implies spectral Riemann-Roch theorems. We regard this result as an instantiation of a 2-dimensional generalized cobordism hypothesis. This perspective draws the result close to many others that generalize results about Euler characteristics and classes to bicategorical traces.
