Parshin's torsion conjecture for algebraic K-groups over finite fields

Let $k$ be a finite field of characteristic $p>0$, and let $X$ be a smooth projective variety over $k$. For each integer $n\geq 1$, let $K_n(X)$ denote the algebraic $K$-group of $X$. Parshin's conjecture. The group $K_n(X)$ is torsion for all integers $n\geq 1$. This conjecture, together with Bass's finite generation conjecture, predicts the structure of algebraic $K$-groups of smooth projective varieties over finite fields. It remains open in general, except when $\text{\rm dim}(X)\leq 1$.