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arXiv · 2504.14383

Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws

Daniel C. Isaksen·Hana Jia Kong·Guchuan Li·Yangyang Ruan·Heyi Zhu
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Abstract

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.

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Daniel C. Isaksen, Hana Jia Kong, Guchuan Li, Yangyang Ruan, Heyi Zhu. 2025-04-19. Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws. https://arxiv.org/abs/2504.14383

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