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arXiv · 2104.02923

On D-modules of categories I

Isamu Iwanari
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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.

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Isamu Iwanari. 2021-04-07. On D-modules of categories I. https://arxiv.org/abs/2104.02923

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