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nLab > Latest Changes: condensed module spectrum

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  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2022

    If possible, please add some indication on where this is headed: Some construction or further development where it’s important that the module spectra are condensed.

    A reference would be great, for instance, where one might see condensed module spectra in action.

    Without any such indication, it feels a little hollow to churn out entries on “condensed Xs” as X varies. See also the comment here.

  3. Added ideas section

    Anonymous

    diff, v2, current

  4. fixing definition according to [this comment]

    Anonymous

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2022

    Same discussion applies as we had in the other thread here.

    I have added a first sentence of the form we had agreed there, and I have removed this line:

    While Peter Scholze’s presentations of condensed mathematics only talks about H-ℤ\mathbb{Z}-module spectra in derived geometry, theoretically one should be able to extend it to general spectra in spectral geometry.

    Because it seems that Peter’s lecture never mentions HℤH\mathbb{Z}-module spectra! In but a footnote it vaguely mentions simplicial abelian groups. From there I had pointed out to you that these may be thought of as presenting HℤH\mathbb{Z}-module spectra.

    diff, v4, current

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