Bökstedt periodicity generator via K-theory

Abstract

For a prime field k of characteristic p > 2, we construct the Bökstedt periodicity generator v ∈ THH₂(k) as an explicit class in the stabilization of K-theory with coefficients K(k, −), and we show directly that v is not nilpotent in THH(k). This gives an alternative proof of the “multiplicative” part of Bökstedt periodicity.