We use trace methods to study the algebraic K-theory of rings of the form R[x1,…, xd ]/(%i,…, xd )2. We compute the relative p-adic K groups for R a perfectoid ring. In particular, we get the integral K groups when R is a finite field, and the integral relative K groups Ks.R^,…, xd]/(x1,…, xd)2, (x1,…, xd)) when R is a perfect Fp-algebra. We conclude with some other notable computations, including some rings which are not quite of the above form.
ASJC Scopus subject areas
- Geometry and Topology