condensed etale cohomology

Stream: maths

[Reid Barton]

Semi-off topic but perhaps of interest to some people here: Can one define the correct l-adic cohomology $H^*_{\mathrm{et}}(X, \mathbb{Z}_l)$, $H^*_{\mathrm{et}}(X, \mathbb{Q}_l)$ using etale sheaves of condensed abelian groups, or does one really have to use the pro-etale site of $X$ (afaik, this was the original purpose for introducing it)?

[Kevin Buzzard]

You're right about the pro-etale site, I have no idea about your question though. Maybe MO?