Near the beginning of Tate's thesis, he showed that the additive group of a complete number field (w.r.t. to any valuation) is Pontryagin self-dual. I am aware of a handful of examples for which it holds, but I would like to know when it holds in general. More precisely, given a group $G$, what are the necessary and sufficient conditions on $G$ for there to exist a topological group isomorphism $G\to\widehat{G}$ ?
2026-03-24 23:51:07.1774396267
Pontryagin Self-Duality
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