Timeline for Derived $\ell$-completion of $\mathbf{Q}_\ell$ sheaf?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2023 at 22:02 | comment | added | Z. M | Constructible sheaves should be much easier, but it should be possible to talk about pro-étale $\mathbb Z$-sheaves being solid, by virtue of the exodromy equivalence which identifies pro-étale $\mathbb Z$-sheaves with (condensed) functors from the Galois (condensed) category to the category of condensed abelian groups. I am not sure how to compare this with solid sheaves in Fargues–Scholze. | |
| Feb 23, 2023 at 0:45 | comment | added | Tomo | That’s an interesting question, as I don’t know that the solid tensor product has been defined outside of the condensed context; i.e. on the pro-étale site of a scheme larger than a point. But I see the resemblance, as in this case we have some $A\in D_{\mathrm{cons}}(X,\mathbf Q_\ell)$ and forming a tensor product with $f^*g_*\mathbf Z_\ell$, so it’s like $\mathbf Q_\ell\otimes\mathbf Z_\ell$ which is what the solid tensor product was devised to handle. | |
| Feb 21, 2023 at 6:59 | comment | added | Z. M | Is that the same as some form of solid tensor product with $f^*g_*\mathbf Q_\ell$? | |
| Feb 20, 2023 at 23:26 | history | answered | Tomo | CC BY-SA 4.0 |