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I have expanded out
H--module spectra in derived geometry
to
-module spectra in derived geometry (via the stable Dold-Kan correspondence)
Let’s see, maybe a better lead-in to this entry could be as follows:
By a condensed spectrum one should generally mean a spectrum in the context of condensed mathematics, hence a spectrum object internal to condensed -groupoids.
A special case of this general notion has essentially been considered in concrete reference goes here: The condensed simplicial abelian groups discussed there may be understood, under the stable Dold-Kan correspondence, to represent (the condensed version of) the particular case of connective -module spectra. These are used to/needed to/desireable for…
Thanks, that’s looking better.
I have adjusted the second paragraph a tad more, pointing within Scholze’s lecture specifically to footnote 12, and trying to indicate that this footnote is far from discussing the definition of a condensed spectrum.
In the same vein, I have added to the References-section the following disclaimer:
A discussion of condensed spectra in the literature seems not to be available yet. For general background on condensed mathematics see: …
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