Cartier modules and cyclotomic spectra

Antieau, Benjamin; Nikolaus, Thomas

doi:10.1090/jams/951

Cartier modules and cyclotomic spectra
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by Benjamin Antieau and Thomas Nikolaus

J. Amer. Math. Soc. 34 (2021), 1-78

DOI: https://doi.org/10.1090/jams/951

Published electronically: December 2, 2020

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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.

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