On the Mixed Tate property and the motivic class of the classifying stack of a finite group

DOI10.2140/ANT.2022.16.2265zbMATH Open1516.14021arXiv2003.10683MaRDI QIDQ6337302

Federico Scavia

Publication date: 24 March 2020

Abstract: Let $G$ be a finite group, and let $B_{mathbbC}G$ the class of its classifying stack $B_{mathbbC}G$ in Ekedahl's Grothendieck ring of algebraic $mathbbC$-stacks $K_0(operatorname{Stacks}_{mathbbC})$. We show that if $B_{mathbbC}G$ has the mixed Tate property, the invariants $H^i(B_{mathbbC}G)$ defined by T. Ekedahl are zero for all $ieq0$. We also extend Ekedahl's construction of these invariants to fields of positive characteristic.

Mathematics Subject Classification ID

Families, moduli, classification: algebraic theory (14J10) (Equivariant) Chow groups and rings; motives (14C15) Generalizations (algebraic spaces, stacks) (14A20) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

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