Good Moduli Spaces in Derived Algebraic Geometry

Eric Ahlqvist; Jeroen Hekking; Michele Pernice; Michail Savvas

doi:10.48550/arxiv.2309.16574

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Good Moduli Spaces in Derived Algebraic Geometry

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Good Moduli Spaces in Derived Algebraic Geometry

Eric Ahlqvist, Jeroen Hekking, Michele Pernice and Michail Savvas

arXiv (Cornell University)

09/28/2023

DOI: 10.48550/arxiv.2309.16574

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli spaces for classical Artin stacks carry over to the derived context. In fact, under natural assumptions, often satisfied in practice, we show that the derived theory essentially reduces to the classical theory. As applications, we establish derived versions of the étale slice theorem for good moduli spaces and the partial desingularization procedure of good moduli spaces.

Mathematics - Algebraic Geometry

Details

Title: Subtitle: Good Moduli Spaces in Derived Algebraic Geometry
Creators: Eric Ahlqvist
Jeroen Hekking
Michele Pernice
Michail Savvas
Resource Type: Preprint
Publication Details: arXiv (Cornell University)
DOI: 10.48550/arxiv.2309.16574
eISSN: 2331-8422
Number of pages: 38 pages
Language: English
Date posted: 09/28/2023
Academic Unit: Mathematics
Record Identifier: 9984696875002771

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