Timeline for Commutation of endomorphisms of abelian varieties
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 30, 2017 at 8:42 | comment | added | Damian Rössler | @ACL: only if $\lambda$ is an isogeny. | |
| Mar 30, 2017 at 8:39 | vote | accept | Damian Rössler | ||
| Mar 29, 2017 at 18:11 | answer | added | R. van Dobben de Bruyn | timeline score: 3 | |
| Mar 29, 2017 at 17:00 | comment | added | ACL | No, not any endomorphism : equality of degrees forces automorphism. | |
| Mar 29, 2017 at 12:58 | history | edited | Damian Rössler | CC BY-SA 3.0 |
I generalised the question, taking into account ACL's counterexample.
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| Mar 29, 2017 at 12:49 | comment | added | Damian Rössler | @ACL: thank you. You are quite right (silly me!). In fact one could replace $-1$ by any endomorphism commuting with $\phi$. I shall modify the question accordingly but I am bit confused about what to expect. | |
| Mar 29, 2017 at 11:47 | comment | added | ACL | Couldn't you have something like $\lambda\circ\phi=- \phi\circ\lambda$ (or, more generally, automorphisms of finite order)? | |
| Mar 29, 2017 at 10:39 | history | asked | Damian Rössler | CC BY-SA 3.0 |