论文标题
在混合泰特属性和有限群体的分类堆栈的动机类别上
On the Mixed Tate property and the motivic class of the classifying stack of a finite group
论文作者
论文摘要
令$ g $为有限的组，让$ \ {b _ {\ mathbb {c}} g \ \} $在ekedahl的grothendieck of Elgebraic $ \ mathbb $ \ mathbb {c} C} c} c}中，其分类stack stack $ b _ {\ mathbb {c}} g $的类别$ k_0（\ operatorName {stacks} _ {\ mathbb {c}}}）$。我们表明，如果$ b _ {\ mathbb {c}} g $具有混合泰特属性，则不变式$ h^i（\ {b _ {\ mathbb {c}} g \ \}）$由T. Ekedahl定义为T. Ekedahl的所有$ i \ neq 0 $为零。我们还将Ekedahl的这些不变性构造扩展到积极特征的领域。
Let $G$ be a finite group, and let $\{B_{\mathbb{C}}G\}$ the class of its classifying stack $B_{\mathbb{C}}G$ in Ekedahl's Grothendieck ring of algebraic $\mathbb{C}$-stacks $K_0(\operatorname{Stacks}_{\mathbb{C}})$. We show that if $B_{\mathbb{C}}G$ has the mixed Tate property, the invariants $H^i(\{B_{\mathbb{C}}G\})$ defined by T. Ekedahl are zero for all $i\neq 0$. We also extend Ekedahl's construction of these invariants to fields of positive characteristic.
