  We prove the Parshin's conjecture on the rational triviality of the higher
algebraic $K$-theory of smooth projective varieties over finite fields. This is
known to imply the Beilinson-Soul\'e conjecture for the fields of positive
characteristic. Especially it implies that for a field $F$ of char $p$ and
$n>0$, the only rationally non-trivial weight appearing in $K_n(F)\otimes
\mathbb{Q}$ can be $n$, thus $K_n(F)\otimes \mathbb{Q}=K_n^M(F)\otimes
\mathbb{Q}$ where $K_n^M(F)$ is the Milnor $K$-theory.
