Timeline for Homomorphisms between Oort–Tate group schemes
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2022 at 15:31 | comment | added | Johan | Yes, very good Tate-Oort indeed. | |
| Jan 21, 2022 at 15:14 | comment | added | Matthieu Romagny | Also even though it doesn't matter much, note that the Tate-Oort paper is authored by John Tate and Frans Oort in that order. | |
| Jan 21, 2022 at 15:14 | comment | added | Matthieu Romagny | In "Moduli of Galois p-covers in mixed characteristics" with Dan Abramovich (Algebra Number Theory 2012) we write this in Definition A.5 + comments after it. But we say hardly more than that! | |
| Jan 21, 2022 at 1:38 | comment | added | Johan | The classification of the group schemes in Oort-Tate uses the decomposition of the Hopf algebra (more precisely the augmentation ideal of this) of the group scheme by eigenspaces for the natural action of $\mathbf{F}_p^*$. So of course any morphism $G \to G'$ gives a corresponding map between the eigenspaces which is what $f$ in the answer above is (by picking the correct eigenspace). This is pretty clear from Lemma 2 of their paper. So I agree with Matthieu that you can't say this isn't in Oort-Tate IMHO. | |
| Jan 20, 2022 at 20:25 | vote | accept | David Loeffler | ||
| Jan 20, 2022 at 20:09 | comment | added | David Loeffler | Oort and Tate just write this down as a bijection on automorphism classes of objects; they don't explicitly state that $G \to (L, a, b)$ is a functor. I'm sure you're correct and it's functorial, but do you know a reference where this is written down explicitly? | |
| Jan 20, 2022 at 19:10 | history | answered | Matthieu Romagny | CC BY-SA 4.0 |