3 problems

Let $X$ be a Noetherian scheme of dimension $d$. For a contravariant functor $F$ on schemes, call $X$ $F$-regular if, for every $r\geq 0$, the map $F(X)\to F(X\times\mathbb{A}^r)$…

Let $X$ be a Noetherian scheme of dimension $d$, and write $K_m(X)$ for its algebraic $K$-groups. A scheme is $K_n$-regular when homotopy invariance holds in degree $n$, equivalent…

Weibel's K-dimensional conjecture. One has