Constructs an involutive duality on condensed spectra with locally compact homotopy groups, extending Pontryagin duality to spectra. Dualization induces Pontryagin duality on homotopy groups with degrees reversed. In particular, every ordinary spectrum, viewed as a discrete condensed spectrum, satisfies biduality without finiteness assumptions.
Resolved Clausen’s Conjecture 5.17 on the local light–profinite structure of smooth For p-adic analytic Artin stacks, the proof includes a generalization of the classical van Dantzig theorem to the case of groupoids and a closed-skeleton reduction. In particular, this result implies that smooth p-adic analytic Artin stacks are !-good.
Uses ∞-topoi to partially characterize the essential image of the derived Stone embedding of the pro-category of π-finite spaces into pyknotic spaces, extending the classical Stone embedding to a derived setting.