5 problems

Generalized opposite-category Farrell–Jones conjecture. The td-group $G$ satisfies this conjecture if, for every Hecke category with $G$-support, the displayed…

COP-Farrell-Jones conjecture for Hecke algebras. For every uniformly regular ring $R$ with $\mathbb{Q} \subseteq R$, the projection

Let $k$ be a regular ring, let $G$ be a torsionfree group, let $\mathrm{B}G$ denote its classifying space, and let $\mathbf{K}(k)$ denote the algebraic $K$-theory spectrum of $k$.…

Let $G$ be a discrete group and let $\mathcal F$ be a family of subgroups of $G$. For a group homomorphism $\varphi:K{\longrightarrow} G$, define the induced family … Let…

Meta-isomorphism conjecture. The assembly map $A_{\mathcal{F}}$ is an isomorphism for every $n\in\mathbb{Z}$.