Timeline for extending homomorphisms of Abelian schemes
Current License: CC BY-SA 3.0
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| Apr 20, 2017 at 5:57 | comment | added | R. van Dobben de Bruyn | To give a concrete example where $\operatorname{Hom}_S(\mathscr A,\mathscr B)$ is not étale even when $S$ is a smooth curve, consider a family $\mathscr A = \mathscr B = \mathscr E$ of elliptic curves whose general member is not CM but a special member $\mathscr E_s$ is. Then $\operatorname{Hom}_S(\mathscr A,\mathscr B) = \operatorname{End}_S(\mathscr E)$ has components lying only over $s$, corresponding to the extra endomorphisms of $\mathscr E_s$. Similar examples exist in mixed characteristic, e.g. if the reduction is supersingular. | |
| Mar 26, 2017 at 6:13 | vote | accept | CommunityBot | moved from User.Id=19475 by developer User.Id=69903 | |
| S Mar 25, 2017 at 21:06 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Mar 25, 2017 at 21:06 | history | made wiki | Post Made Community Wiki by Jason Starr |