Cartier modules and cyclotomic spectra

Antieau, Benjamin; Nikolaus, Thomas

doi:10.1090/jams/951

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Cartier modules and cyclotomic spectra

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Antieau, Benjamin
Max Planck Institute for Mathematics, Max Planck Society;

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Nikolaus, Thomas
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/jams/951
(Publisher version)

https://doi.org/10.48550/arXiv.1809.01714
(Preprint)

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Citation

Antieau, B., & Nikolaus, T. (2021). Cartier modules and cyclotomic spectra. Journal of the American Mathematical Society, 34(1), 1-78. doi:10.1090/jams/951.

Cite as: https://hdl.handle.net/21.11116/0000-0008-021D-6

Abstract

We construct and study a t-structure on p-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t-structure. Our main tool is a new approach to p-typical cyclotomic spectra via objects we call p-typical topological Cartier modules. Using these, we prove that the heart of the cyclotomic t-structure is the full subcategory of derived V-complete objects in the abelian category of p-typical Cartier modules.