On D-modules of categories I
Algebraic Geometry
2022-03-01 v2
Abstract
In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is based on a canonical extension of factorization homology to the mapping stack and relation between sheaves on free loop space and D-modules. The second one uses the algebraic structure on Hochschild pairs, its moduli-theoretic interpretation, Kodaira-Spencer morphisms, and the relation between dg Lie algebras and pointed formal stacks.
Cite
@article{arxiv.2104.02923,
title = {On D-modules of categories I},
author = {Isamu Iwanari},
journal= {arXiv preprint arXiv:2104.02923},
year = {2022}
}