Timeline for A morphism of elliptic schemes that preserves the identity is a homomorphism
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| Jan 26, 2015 at 22:30 | comment | added | user74230 | @LisaS.: Note that just above section 6.1 Mumford imposed the standing hypothesis that schemes he considers are all locally noetherian and separated (the archaic distinction of pre-schemes and schemes in original EGA terminology), so in that sense the missing hypothesis was that $p$ is locally of finite type. | |
| Jan 26, 2015 at 22:14 | comment | added | Lisa S. | @user74230: The proof in GIT is indeed cleaner, thank you. Though in 6.1 2) there, I think one has to assume in addition that $p$ is locally of finite presentation (to ensure the openness of $p$ used in the proof); this, of course, is harmless in the view of the subsequent discussion. | |
| Jan 26, 2015 at 11:52 | comment | added | Joe Silverman | Although it's just over fields, the proof that this is true for abelian varieties given in Mumford's Abelian Varieties via a rigidity argument is also quite enlightening. | |
| Jan 26, 2015 at 5:34 | comment | added | user74230 | Read the proof for abelian schemes in Chapter 6 of GIT. The rigidity technique there is easier to understand. | |
| Jan 26, 2015 at 4:04 | history | asked | Lisa S. | CC BY-SA 3.0 |