Timeline for l-adic vs complex Perverse Sheaves
Current License: CC BY-SA 3.0
4 events
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| Oct 18, 2011 at 20:47 | comment | added | Alex | Sorry for the typos. Not sure what happened to the last formula. Anyway, let me reformulate it in words : $a$ is an $\ell$-adic unit. | |
| Oct 18, 2011 at 20:46 | comment | added | Alex |
Yes. If ou just take $X=\mathbb{G}_m$, then the toplogical fundamental group is $\mathbb{Z}$, and a rank 1 local system of $\overline{Q}_\ell$ on $X_{an}$ corresponds to a representation of $\mathbb{Z}$ on $\overline{Q}_\ell$, i.e., an element $a$ of $\overline{Q}_\ell$. The local system comes from an étale local system on $X$ if and only if the representation extends to $\widehat{\mathbb{Z}}$, that is, if and only if $a\in\overline{\mathbb{Z}}_\ell^\times$.
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| Oct 18, 2011 at 17:57 | comment | added | Keerthi Madapusi | Just to clarify: Is the basic point that you'd like your local system to come from a representation of the full pro-finite fundamental group, and not just the topological fundamental group? | |
| Oct 18, 2011 at 13:09 | history | answered | naf | CC BY-SA 3.0 |