3 problems

Let $X$ be a noetherian scheme of dimension at most $d$, and let $\text{K}_{-d}(X)$ and $\text{KH}_{-d}(X)$ denote algebraic and homotopy algebraic $K$-theory in degree $-d$. Weibe…

Let $R$ be a regular ring with $\mathbb Q\subseteq R$, let $G$ be a group, and let $n\in\mathbb Z$. Write $NK_n(RG)$ for the relevant Nil-group and $KH_n(RG)$ for homotopy $K$-theo…

Fibered homotopy K-theory isomorphism conjecture. The group $G$ satisfies the (fibered) $\mathit{KH}$-isomorphism conjecture for $R$ if the pair $(G,\mathcal{FIN})$ satisfies the (…