Parshin猜想的证明
Proof of the Parshin's Conjecture
摘要：
证明了关于有限域上光滑投射簇的高等代数$K$ -理论的有理平凡性的Parshin猜想.这是已知的暗示贝林森-苏莱猜想的领域的积极特征。特别地，它意味着对于char $p$和$n>0$的域$F$，在$K_n(F)\otimes \mathbb{Q}$中出现的唯一有理非平凡权重可以是$n$，因此是$K_n(F)\otimes \mathbb{Q}=K_n^M(F)\otimes \mathbb{Q}$，其中$K_n^M(F)$是Milnor $K$ -理论。
英文摘要：
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.
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