Artin--Mazur formal groups and Milne duality via unipotent spectra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912633582518272 |
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| author | Mondal, Shubhodip Moulinos, Tasos Yang, Lucy |
| author_facet | Mondal, Shubhodip Moulinos, Tasos Yang, Lucy |
| contents | We introduce and develop the notion of "unipotent spectra." This is defined to be the stabilization of Toën's category of affine stacks, and is related to recent work of Mondal--Reinecke. Unipotent spectra give rise to unipotent stable homotopy groups and unipotent homology, which are new invariants for schemes valued in unipotent group schemes. As applications, we recover the Artin--Mazur formal groups associated to schemes without any vanishing assumptions. Further, we show that syntomic cohomology admits a natural refinement to a perfect unipotent spectrum. Finally, we extend Milne's work on arithmetic duality theorems to the category of perfect unipotent spectra and apply it to refine Poincaré duality in syntomic cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Artin--Mazur formal groups and Milne duality via unipotent spectra Mondal, Shubhodip Moulinos, Tasos Yang, Lucy Algebraic Geometry Algebraic Topology 14A30, 14F35, 14F30, 55U30 We introduce and develop the notion of "unipotent spectra." This is defined to be the stabilization of Toën's category of affine stacks, and is related to recent work of Mondal--Reinecke. Unipotent spectra give rise to unipotent stable homotopy groups and unipotent homology, which are new invariants for schemes valued in unipotent group schemes. As applications, we recover the Artin--Mazur formal groups associated to schemes without any vanishing assumptions. Further, we show that syntomic cohomology admits a natural refinement to a perfect unipotent spectrum. Finally, we extend Milne's work on arithmetic duality theorems to the category of perfect unipotent spectra and apply it to refine Poincaré duality in syntomic cohomology. |
| title | Artin--Mazur formal groups and Milne duality via unipotent spectra |
| topic | Algebraic Geometry Algebraic Topology 14A30, 14F35, 14F30, 55U30 |
| url | https://arxiv.org/abs/2510.06152 |