分次单参数子群及其检测性质
Graded 1-parameter subgroups and detection properties
摘要：
我们利用表示论的工具来更好地理解分次群概型的上同调。为此，我们将注意力集中在基场具有特征$p > 0$的情况。受Friedlander等人工作的启发，我们建立了分次$1$ -参数子群的理论，记为$V_r^*(G)$ .给出了双分次$\boldsymbol{\rm k}$ -代数$ψ: H^{*, *}(G, \boldsymbol{\rm k}) \to \boldsymbol{\rm k}[V_r^* (G)],$的一个自然同态，其中$\boldsymbol{\rm k}[V_r^* (G)]$是$V_r^*(G)$的双分次坐标环.证明了一类分次群格式的$ψ$是一个$F$ -单态.这提供了证据表明，与适当的检测性能，Quillen型的结果可能存在的分级组计划。
英文摘要：
We use tools of representation theory to get a better understanding of the cohomology of graded group schemes. For that, we focus our attention on the case in which the base field is of characteristic $p > 0$. Using as inspiration the work of Friedlander, et al, we build the theory of graded $1$-parameter subgroups denoted by $V_r^*(G)$. We give a natural homomorphism of bigraded $\boldsymbol{\rm k}$-algebras $ψ: H^{*, *}(G, \boldsymbol{\rm k}) \to \boldsymbol{\rm k}[V_r^* (G)],$ where $\boldsymbol{\rm k}[V_r^* (G)]$ is the bigraded coordinate ring for $V_r^*(G)$. We show that $ψ$ is an $F$-monomorphism for a class of graded group schemes. This provides evidence that with the appropriate detection property, a Quillen-type result could exist for graded group schemes.
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