Work

Analytification of mapping stacks

Year: 2024

Type: article

Abstract: Derived mapping stacks are a fundamental source of examples of derived enhancements of classical moduli problems.For instance, they appear naturally in Gromov-Witten theory and in some branches of geometric representation theory.In this paper we show that in many cases the mapping stack construction commutes with the (complex or nonarchimedean) derived analytification functor.Along the way, we establish several new foundational results in derived analytic geometry that are likely to be useful elsewhere.For instance, we provide a C-analytic version of Kiehl's theorem for (derived) compact Stein spaces, and study some incarnations of analytic Tannaka duality.We apply these results to the study of the Riemann-Hilbert correspondence and the derived period domain.

Source: Algebraic geometry

DOI: 10.14231/ag-2025-002

Authors: Julian Holstein, Mauro Porta

Institutions: Institut de Recherche Mathématique Avancée, Université de Strasbourg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: University of Pennsylvania, London Mathematical Society, Deutsche Forschungsgemeinschaft, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Awards: G432818845, EXC 2121: Quantum Universe