Parshin's conjecture
In mathematics, more specifically in algebraic geometry, Parshin's conjecture states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion:
See Conjecture 51 in.
It is named after Aleksei Nikolaevich Parshin and Alexander Beilinson.The conjecture holds if by Quillen's computation of the K-groups of finite fields, showing in particular that they are finite groups.Curves
The conjecture holds if by the proof of Corollary 3.2.3 of Harder.
Additionally, by Quillen's finite generation result it follows that the K-groups are finite if.
