The Morel-Voevodsky Construction over Algebraic Stacks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915590988365824 |
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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 |