Groups of order p³ are mixed Tate

2015/03/13 by Pădurariu, Tudor
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1503.04235

Abstract

A natural place to study the Chow ring of the classifying space BG, for G a linear algebraic group, is Voevodsky's triangulated category of motives, inside which Morel and Voevodsky, and Totaro have defined motives M(BG) and M^c(BG), respectively. We show that, for any group G of order p³ over a field of characteristic not p which contains a primitive p²-th root of unity, the motive M(BG) is a mixed Tate motive. We also show that, for a finite group G over a field of characteristic zero, M(BG) is a mixed Tate motive if and only M^c(BG) is a mixed Tate motive.

Related

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• Higher Tate traces of Chow motives
• Groupes fondamentaux motiviques de Tate mixte
• Mixed Tate motives over \Z
• On the Problem of Mixed-Tateness of the Motives of G-Varieties