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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 27th 2014
• (edited Aug 27th 2014)

I gave Pontryagin duality for torsion abelian groups its own entry, cross-linked of course with the examples-section at Pontryagin dual and with all other relevant entries.

Mainly I wanted to record this diagram here in a way that one could link to it quasi-directly:

$\array{ &\mathbb{Z}[p^{-1}]/\mathbb{Z} &\hookrightarrow& \mathbb{Q}/\mathbb{Z} &\hookrightarrow& \mathbb{R}/\mathbb{Z} \\ {}^{\mathllap{hom(-,\mathbb{R}/\mathbb{Z})}}\downarrow \\ &\mathbb{Z}_p &\leftarrow& \hat \mathbb{Z} &\leftarrow& \mathbb{Z} }$
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 8th 2022

I notice that none of the three references currently given at Pontryagin duality for torsion abelian groups really seem to substantiate the main claims made in the entry, and only

• Dinakar Ramakrishnan, Robert J. Valenza, Section 3 of: Fourier Analysis on Number Fields, Graduate Texts in Mathematics 186, Springer 1999 (doi:10.1007/978-1-4757-3085-2)

provides any relevant details at all.

Maybe there is a more focused reference on the entry’s topic?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 8th 2022

for when the editing functionality is back: