论文标题
parshin猜想的证明
Proof of the Parshin's Conjecture
论文作者
论文摘要
我们证明了山看着较高代数$ k $的理性琐事的猜想 - 有限领域的光滑投射品种的理论。众所周知，这暗示着贝林森 - 苏尔的猜想是积极特征的领域。特别是这意味着对于$ f $ char $ p $和$ n> 0 $，唯一出现在$ k_n（f）\ otimes \ mathbb {q} $中的唯一合理非平凡的重量可以是$ n $，因此可以是$ n $，因此$ k_n（f）\ otimes \ otimes \ otimes \ athbb {q} = Q} = k_n^m（q Q artime） $ k_n^m（f）$是milnor $ k $ - 理论。
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-Soulé 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.
