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Cartier modules and cyclotomic spectra


Authors: Benjamin Antieau and Thomas Nikolaus
Journal: J. Amer. Math. Soc. 34 (2021), 1-78
MSC (2010): Primary 14F30, 14L05, 13D03
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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Additional Information

Benjamin Antieau
Affiliation: Department of Mathematics, University of Illinois at Chicago, Statistics and Computer Science, 851 South Morgan Street, Chicago, Illinois, 60607 – and – Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208
Email: antieau@northwestern.edu

Thomas Nikolaus
Affiliation: FB Mathematik und Informatik, Universität Münster, Einsteinstrasse 62 D-48149 Münster, Germany
Email: nikolaus@uni-muenster.de

DOI: https://doi.org/10.1090/jams/951
Keywords: Topological Hochschild homology, cyclotomic spectra, Cartier modules, Dieudonn\'e modules, de Rham--Witt complexes.
Received by editor(s): October 5, 2018
Received by editor(s) in revised form: January 8, 2020
Published electronically: December 2, 2020
Additional Notes: The first author was supported by NSF Grant DMS-1552766.
Article copyright: © Copyright 2020 American Mathematical Society