The derived category of complex periodic K-theory localized at an odd prime

TL;DR

This paper proves that for odd primes, the derived category of p-local complex periodic K-theory is equivalent to the derived category of its homotopy ring, showing it is algebraic.

Contribution

It establishes a triangulated equivalence between the derived category of p-local complex K-theory and the derived category of its homotopy ring for odd primes.

Findings

Derived category of KU_{(p)} is equivalent to the derived category of its homotopy ring.

The triangulated category is algebraic for odd primes.

Provides a new understanding of the structure of p-local complex K-theory.

Abstract

We prove that for an odd prime $p$, the derived category $\mathcal{D}(KU_{(p)})$ of the $p$-local complex periodic $K$-theory spectrum $KU_{(p)}$ is triangulated equivalent to the derived category of its homotopy ring $\pi_*KU_{(p)}$. This implies that if $p$ is an odd prime, the triangulated category $\mathcal{D}(KU_{(p)})$ is algebraic.