Floor, ceiling, slopes, and $K$-theory
K-Theory and Homology
2023-08-30 v2 Algebraic Topology
Number Theory
Abstract
We calculate by evaluating the syntomic cohomology 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 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.
Cite
@article{arxiv.2110.04978,
title = {Floor, ceiling, slopes, and $K$-theory},
author = {Yuri J. F. Sulyma},
journal= {arXiv preprint arXiv:2110.04978},
year = {2023}
}
Comments
v2: expanded exposition; added link to interactive figures/source code; fixed wildly incorrect mod-p multiplicative structure. 24 pages, 8 figures