Papers › Floor, ceiling, slopes, and K-theory
Floor, ceiling, slopes, and K-theory
Yuri J. F. Sulyma
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We calculate K_*(k[x]/xᵉ;𝐙ₚ) by evaluating the syntomic cohomology 𝐙ₚ(i)(k[x]/xᵉ) introduced by Bhatt-Morrow-Scholze and Bhatt-Scholze. This recovers calculations of Hesselholt-Madsen and Speirs, and generalizes an example of Mathew treating the case e=2 and p>2. Our main innovation is systematic use of the floor and ceiling functions, which clarifies matters substantially even for e=2. We furthermore observe a persistent phenomenon of slopes. As an application, we answer some questions of Hesselholt.
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