Timeline for Derived $\ell$-completion of $\mathbf{Q}_\ell$ sheaf?
Current License: CC BY-SA 4.0
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| Jul 21, 2023 at 0:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 23, 2023 at 0:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 20, 2023 at 23:26 | answer | added | Tomo | timeline score: 1 | |
| Dec 5, 2022 at 0:41 | comment | added | Tomo | Thank you @D.-C.Cisinski, that completely clarifies the confusion of my second paragraph. | |
| Dec 4, 2022 at 11:00 | comment | added | D.-C. Cisinski | In fact, one can also see this in a more elementary way. See Section B.2 in this paper: cambridge.org/core/journals/compositio-mathematica/article/… | |
| Dec 4, 2022 at 10:39 | comment | added | D.-C. Cisinski | Hence, at the end of the day, $D_{cons}(X,\mathbf{Q}_\ell)$ has the same objects as $D_{cons}(X,\mathbf{Z}_\ell)$ and the mapping spaces of $D_{cons}(X,\mathbf{Q}_\ell)$ are those of $D_{cons}(X,\mathbf{Z}_\ell)$ tensored by $\mathbf{Q}$. | |
| Dec 4, 2022 at 10:34 | comment | added | D.-C. Cisinski | For references: Theorem 2.35 in Benjamin Antieau, David Gepner, Jeremiah Heller arxiv.org/abs/1610.07207 for the vanishing of $K_{-1}$. For the interpretation of $K_{-1}=0$ in terms of Verdier quotients, this is in the paper of Marco Schlichting Negative K-theory of derived categories (end of Section 1). | |
| Dec 4, 2022 at 10:26 | comment | added | D.-C. Cisinski | In fact, since $D_{cons}(X,\mathbf{Z}_\ell)$ has a bounded $t$-structure, we have a vanishing $K$-group in degree $-1$: $K_{-1}(D_{cons}(X,\mathbf{Z}_\ell))=0$. That means precisely that all the Verdier quotients of $D_{cons}(X,\mathbf{Z}_\ell)$ already are idempotent complete. | |
| Dec 4, 2022 at 7:17 | history | edited | Tomo | CC BY-SA 4.0 |
Second paragraph had some nonsense
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| Dec 4, 2022 at 2:32 | history | asked | Tomo | CC BY-SA 4.0 |