Floor, ceiling, slopes, and $K$-theory

Yuri J. F. Sulyma

We calculate ${\mathrm{K}}_{\ast }(k[x]/x^e;{\mathbf{Z}}_p)$ by evaluating the syntomic cohomology ${\mathbf{Z}}_p(i)(k[x]/x^e)$ introduced by Bhatt-Morrow-Scholze and Bhatt-Scholze. This recover…