Abstract

We calculate ${K<!--FUNCTION\; APPLICATION-->}_{\ast }(k[x]∕x^e;{\mathbb{Z}}_p)$ 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 $e=2$ 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.

Keywords

Mathematical Subject Classification

Supplementary material

Times tables for K

Milestones

Authors