Timeline for Lifting of Frobenius on semi-abelian varieties
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2016 at 6:09 | vote | accept | SashaP | ||
| Mar 12, 2016 at 14:18 | answer | added | Piotr Achinger | timeline score: 4 | |
| Mar 12, 2016 at 14:10 | comment | added | Piotr Achinger | What do you mean by `$A$ lifts to $W(k)$'? Do you want the lift to be a scheme or a formal scheme? | |
| Mar 9, 2016 at 4:24 | comment | added | nfdc23 | I assume $k$ is perfect. Let $A'$ be the chosen lift of $A$, giving $B'$ and $T'$ lifting $B$ and $T$ respectively. Using the canonical link between such extensions and line bundles on $B'$ arising from the dual abelian scheme when $T = {\rm{GL}}_1$ (so we can regard $B'$ as primary and $A'$ as secondary), in general $A'$ corresponds to a $W(k)$-point $\xi$ of ${B'}^{\vee} \otimes {\rm{X}}^{\ast}(T)$ (using the dual abelian scheme). So the necessary and sufficient condition is that Frobenius of $B$ lifts to $B'$ and its dual map along with Frobenius for $T$ carries $\xi^{(p)}$ to $\xi$. | |
| Mar 8, 2016 at 21:03 | history | asked | SashaP | CC BY-SA 3.0 |