The Cauchy problem for D-modules on Ran spaces
G.Bonavolont\`a
TL;DR
This paper develops an elementary framework for D-modules on Ran spaces using two-limits, defining key concepts and proving a fundamental theorem in this setting.
Contribution
It introduces a novel elementary approach to D-modules on Ran spaces and proves the Cauchy-Kowaleski-Kashiwara theorem within this framework.
Findings
Defined the category of coherent D-modules on Ran spaces
Established characteristic varieties and non-characteristic maps in this context
Proved the Cauchy-Kowaleski-Kashiwara theorem for D-modules on Ran spaces
Abstract
We will adopt an elementary approach to D-modules on Ran spaces in terms of two-limits; the aim here is to define the category of coherent D-modules, characteristic varieties and non-characteristic maps. An application will be the proof of the Cauchy-Kowaleski-Kashiwara theorem in this setting.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology · Mathematical Analysis and Transform Methods