Condensed Brown Comenetz Duality

Abstract

We construct an involutive duality on condensed spectra with locally compact homotopy groups, extending classical Pontryagin duality. We prove that dualization induces Pontryagin duality on homotopy groups, with degrees reversed, and that the canonical biduality map is an equivalence. In particular, every ordinary spectrum, viewed as a discrete condensed spectrum, satisfies biduality, without any finiteness assumptions on its homotopy groups.