I've heard/read it said many times that "the good notion of quasi-coherent sheaf for complex manifolds is that of a Fréchet quasi-coherent sheaf", and the standard citation to which I've been pointed is Eschmeier and Putinar's book Spectral Decompositions And Analytic Sheaves.

There, in Section 4.6, we find the following quote:

The literature concerning quasi-coherent analytic Fréchet sheaves is not so plentiful, and is always related to concrete applications. We mention only the article of Ramis and Ruget (1974), where this class of sheaves was introduced, and a monograph on deformation theory by Bingener and Kosarew (1987) where this class of sheaves is used for other applications.

The article of Ramis and Ruget is "Résidus et dualité", and the one of Bingener and Kosarew is Lokale Modulräume in der analytischen Geometrie, Volume 2 (ISBN: 3528063017). The latter is a ~700 page book in German, and the combination of the length and language make it a... difficult reference for me to get much out of. This is particularly annoying because I would love to know about the "other applications" for which they use quasi-coherent analytic sheaves.

Question. Are there any "modern" references for the theory of quasi-coherent analytic sheaves?

I have also been told a few times that the theory of condensed/liquid things can provide a different approach, avoiding the need for quasi-coherent analytic sheaves, but I've never found a reference that explains why this is so (in particular, this would count as a "modern" reference for quasi-coherent analytic sheaves).

I've heard/read it said many times that "the good notion of quasi-coherent sheaf for complex manifolds is that of a Fréchet quasi-coherent sheaf", and the standard citation to which I've been pointed is Eschmeier and Putinar's book Spectral Decompositions And Analytic Sheaves.

There, in Section 4.6, we find the following quote (emphasis mine):

The literature concerning quasi-coherent analytic Fréchet sheaves is not so plentiful, and is always related to concrete applications. We mention only the article of Ramis and Ruget (1974), where this class of sheaves was introduced, and a monograph on deformation theory by Bingener and Kosarew (1987) where this class of sheaves is used for other applications.

The article of Ramis and Ruget is "Résidus et dualité", and the one of Bingener and Kosarew is Lokale Modulräume in der analytischen Geometrie, Volume 2 (ISBN: 3528063017). The latter is a ~700 page book in German, and the combination of the length and language make it a... difficult reference for me to get much out of. This is particularly annoying because I would love to know about the "other applications" for which they use quasi-coherent analytic sheaves.

Question. Are there any "modern" references for the theory of quasi-coherent analytic sheaves?

I have also been told a few times that the theory of condensed/liquid things can provide a different approach, avoiding the need for quasi-coherent analytic sheaves, but I've never found a reference that explains why this is so (in particular, this would count as a "modern" reference for quasi-coherent analytic sheaves).