A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs

Fuente: arXiv
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Main Author: Savage, Rhiannon
Format: Preprint
Published: 2026
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author Savage, Rhiannon
author_facet Savage, Rhiannon
contents Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show that representability naturally follows from an Artin-Lurie style representability theorem. This necessitates the development of a new model for derived differential geometry using an extension of $C^\infty$-rings that we call $C^\infty$-bornological rings. This new theory embeds into the theory of derived bornological geometry recently proposed by Ben-Bassat, Kelly, and Kremnizer.
format Preprint
id arxiv_https___arxiv_org_abs_2604_24164
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs
Savage, Rhiannon
Algebraic Geometry
Category Theory
Differential Geometry
14D23, 18F20, 18N60
Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show that representability naturally follows from an Artin-Lurie style representability theorem. This necessitates the development of a new model for derived differential geometry using an extension of $C^\infty$-rings that we call $C^\infty$-bornological rings. This new theory embeds into the theory of derived bornological geometry recently proposed by Ben-Bassat, Kelly, and Kremnizer.
title A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs
topic Algebraic Geometry
Category Theory
Differential Geometry
14D23, 18F20, 18N60
url https://arxiv.org/abs/2604.24164