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Abstract
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We calculate
by evaluating the syntomic cohomology
introduced by Bhatt, Morrow and Scholze. This recovers calculations of Hesselholt,
Madsen and Speirs and generalizes an example of Mathew treating the case
and
. Our main
innovation is systematic use of the floor and ceiling functions, which clarifies matters substantially
even for
.
We furthermore observe a persistent phenomenon of
slopes. As an application, we
answer some questions of Hesselholt.
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Keywords
K-theory, truncated polynomials, prismatic cohomology,
syntomic cohomology, crystalline cohomology
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Mathematical Subject Classification
Primary: 14F30, 19D55, 19E15
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Supplementary material
Times tables for
K
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Milestones
Received: 14 December 2021
Revised: 22 January 2023
Accepted: 31 May 2023
Published: 27 August 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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