Timeline for Some naive questions about pro-etale cohomology
Current License: CC BY-SA 4.0
4 events
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| Apr 15 at 11:13 | comment | added | Peter Scholze | There is a fully faithful embedding of etale sheaves into pro-etale sheaves, and this preserves cohomology, see Proposition 5.2.6 (2) of The pro-etale topology for schemes. This applies in particular to $\mathbb Z$ or $\mathbb G_m$, so their pro-etale cohomology agrees with the usual etale cohomology. The pro-etale $\pi_1$ is a red herring for these questions. | |
| Apr 13 at 20:37 | comment | added | R. van Dobben de Bruyn | I think that $H^1_{\text{proét}}(X,\mathbf Z)$ should be nonzero when $X$ is a nodal cubic, since (the pro-discrete completion of?) its pro-étale fundamental group is the discrete group $\mathbf Z$ (by Lemma 7.4.6 in Bhatt–Scholze). | |
| Apr 13 at 18:37 | history | edited | Krill | CC BY-SA 4.0 |
added 67 characters in body
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| Apr 13 at 4:57 | history | asked | Krill | CC BY-SA 4.0 |