Riemann-Roch theorems in monoidal 2-categories

Autor:	Campbell, Jonathan A., Ponto, Kate
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Mathematics - Algebraic Geometry Mathematics - Category Theory Mathematics - K-Theory and Homology 19L10 18N10 16E40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 38 pages, added references to arXiv:1210.1174
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.04351 Zobrazit plný text záznamu View this record from Arxiv