Timeline for $\mathbb Q_p$ étale local sytem in characteristic $p>0$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2017 at 10:38 | comment | added | Emiliano Ambrosi | Sorry for my late answer. I was wondering what happens for the elliptic curves without p-torsion defined over the separable closure of K. I have the impression that in this situation the action of the Galois group is trivial on the p-adic Tate module. What it is wrong? They are all isotrivial? | |
| Oct 14, 2017 at 10:36 | vote | accept | Emiliano Ambrosi | ||
| Apr 5, 2017 at 21:02 | comment | added | nfdc23 | If $h:Y' \rightarrow Y$ is a universal homeomorphism of schemes (equivalently: surjective, radiciel, integral) then $U \rightsquigarrow U \times_Y Y'$ is an equivalence of etale sites, and in particular if $F$ is an abelian etale sheaf on $Y$ then ${\rm{H}}^i(Y,F) \rightarrow {\rm{H}}^i(Y',h^*F)$ is an isomorphism. By sheafifying, higher direct images along any map $X \rightarrow Y$ are "unaffected" by base change along $h$. In particular, your question (2) is the same over the perfect closure of $k$ as over $k$, and over the perfect closure the connected-etale sequence splits, etc. | |
| Apr 5, 2017 at 16:17 | comment | added | Emiliano Ambrosi | Thank you very much! for 2) for me almost trivial means that the image of the representation is finite (I will edit). Have you a reference for the fact that "a non-isotrivial pencil of ordinary elliptic curves the resulting representation into Z_p^* typically has open image."? My worries were about the possible fact that an abelian variety over kk could have all the pp power torsion defined over purely inseparable extensions, and hence that the action of the galois could be trivial on it. Thank you! | |
| S Apr 5, 2017 at 15:57 | history | answered | nfdc23 | CC BY-SA 3.0 | |
| S Apr 5, 2017 at 15:57 | history | made wiki | Post Made Community Wiki by nfdc23 |