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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.
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BibTeX
@misc{helor2026condensed,
title = {{Condensed Brown Comenetz Duality}},
author = {Roey Hel-Or and Amos Kaminski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18162},
eprint = {2609.18162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18162},
}
RIS
TY - UNPB
TI - Condensed Brown Comenetz Duality
AU - Roey Hel-Or
AU - Amos Kaminski
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18162
UR - https://arxiv.org/abs/2609.18162
AB - 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.
ER -