Timeline for Topology on $p$-adic period rings in an article by Fontaine, part II
Current License: CC BY-SA 4.0
4 events
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| Jun 26, 2021 at 19:48 | comment | added | Peter Scholze | Dustin, thanks for this! I agree that the condensed perspective is (to me) helpful for not getting bogged down in topological subtleties. @Z. M: This must refer to the "old" pro-etale site; for almost all purposes, that's best forgotten. With the "new" pro-etale site (as in the work on diamonds), everything should be OK. | |
| Jun 25, 2021 at 18:49 | comment | added | Z. M | I wonder how one compares pro-étale stuff for adic spaces and condensed mathematics. I heard that pro-étale stuff for adic spaces is slightly different from that for schemes, and in particular, the topos is not replete, and the $\mathbb A_{\operatorname{inf}}$-sheaf needs to be sheafified. When we want to take sheaves on adic spaces valued in condensed world, what are correct options? | |
| Jun 25, 2021 at 18:36 | comment | added | Z. M | A remark on tilting and Witt vectors. Let $R:=\mathcal O_{\mathbb C_p}$. The tilt $R^\flat$ is performed in the condensed world (in particular, it is not discrete), and the Witt vectors are taken pointwise on the sheaf, and if I am not mistaken, the resulting presheaf is a sheaf, since the functor $W$ is a right adjoint therefore preserves small limits. | |
| Jun 25, 2021 at 17:46 | history | answered | Dustin Clausen | CC BY-SA 4.0 |