2024/06/27 by Chan, David, Vogeli, Chase · 1 citation
#19D50 (Primary) #19L47 #55P91 #55Q91 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2406.19481
We compute the RO(G)-graded equivariant algebraic K-groups of a finite field with an action by its Galois group G. Specifically, we show these K-groups split as the sum of an explicitly computable term and the well-studied RO(G)-graded coefficient groups of the equivariant Eilenberg--MacLane spectrum H\underline\mathbb Z. Our comparison between the equivariant K-theory spectrum and H\underline\mathbb Z further shows they share the same Tate spectra and geometric fixed point spectra. In the case where G has prime order, we provide an explicit presentation of the equivariant K-groups.