Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910916759519232 |
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| author | Isaksen, Daniel C. Kong, Hana Jia Li, Guchuan Ruan, Yangyang Zhu, Heyi |
| author_facet | Isaksen, Daniel C. Kong, Hana Jia Li, Guchuan Ruan, Yangyang Zhu, Heyi |
| contents | We describe some periodic structure in the cohomology of the moduli stack of 1-dimensional formal group laws, also known as the $E_2$-page of the classical Adams--Novikov spectral sequence. This structure is distinct from the familiar $v_n$-periodicities, and it displays interesting number-theoretic properties. Our techniques involve the $\mathbb{C}$-motivic Adams spectral sequence, and we obtain analogous periodic structure in $\mathbb{C}$-motivic stable homotopy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws Isaksen, Daniel C. Kong, Hana Jia Li, Guchuan Ruan, Yangyang Zhu, Heyi Algebraic Topology Primary 55T15, 14F42, Secondary 55Q51 We describe some periodic structure in the cohomology of the moduli stack of 1-dimensional formal group laws, also known as the $E_2$-page of the classical Adams--Novikov spectral sequence. This structure is distinct from the familiar $v_n$-periodicities, and it displays interesting number-theoretic properties. Our techniques involve the $\mathbb{C}$-motivic Adams spectral sequence, and we obtain analogous periodic structure in $\mathbb{C}$-motivic stable homotopy. |
| title | Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws |
| topic | Algebraic Topology Primary 55T15, 14F42, Secondary 55Q51 |
| url | https://arxiv.org/abs/2504.14383 |