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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:

    [p 1]/ / / hom(,/) p ^ \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:

    A good reference is instead:

    • Luis Ribes, Pavel Zalesskii, Thm. 2.9.6 in: Profinite Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge: A Series of Modern Surveys in Mathematics), vol 40. Springer 2000 (doi:10.1007/978-3-662-04097-3_2)
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