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Main Authors: Deshmukh, Neeraj, Sefzig, Felix
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.12820
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author Deshmukh, Neeraj
Sefzig, Felix
author_facet Deshmukh, Neeraj
Sefzig, Felix
contents In this article, we give a construction of the (un-)stable motivic homotopy category of an algebraic stack in the spirit of Morel-Voevodsky. We prove that this new construction agrees with the stable motivic homotopy category defined by Chowdhury and D'Angelo. As an application, we extend Bachmann's spectral rigidity theorem to algebraic stacks. Moreover, we extend the construction of the framed motivic homotopy category to algebraic stacks and prove Hoyois' Reconstruction Theorem in this setting. Finally, we discuss an extension of the formalism of cocomplete coefficient systems à la Drew-Gallauer to algebraic stacks.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12820
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Morel-Voevodsky Construction over Algebraic Stacks
Deshmukh, Neeraj
Sefzig, Felix
Algebraic Geometry
In this article, we give a construction of the (un-)stable motivic homotopy category of an algebraic stack in the spirit of Morel-Voevodsky. We prove that this new construction agrees with the stable motivic homotopy category defined by Chowdhury and D'Angelo. As an application, we extend Bachmann's spectral rigidity theorem to algebraic stacks. Moreover, we extend the construction of the framed motivic homotopy category to algebraic stacks and prove Hoyois' Reconstruction Theorem in this setting. Finally, we discuss an extension of the formalism of cocomplete coefficient systems à la Drew-Gallauer to algebraic stacks.
title The Morel-Voevodsky Construction over Algebraic Stacks
topic Algebraic Geometry
url https://arxiv.org/abs/2506.12820