Bokstedt periodicity generator via K-theory

TL;DR

This paper constructs an explicit generator for B"okstedt periodicity in the topological Hochschild homology of a prime field, providing a new proof of its multiplicative structure.

Contribution

It explicitly constructs the B"okstedt periodicity generator in K-theory with coefficients and proves its non-nilpotency, offering an alternative proof of B"okstedt periodicity.

Findings

Explicit construction of the B"okstedt periodicity generator

Proof that the generator is not nilpotent in THH

Alternative proof of B"okstedt periodicity's multiplicative part

Abstract

For a prime field $k$ of characteristic $p > 2$, we construct the B\"okstedt periodicity generator $v \in THH_2(k)$ 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 B\"okstedt periodicity.