Parshin's conjecture

In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion:^[1]

${\displaystyle K_{i}(X)\otimes \mathbf {Q} =0,\ \,i>0.}$

It is named after Aleksei Nikolaevich Parshin and Alexander Beilinson.