Timeline for $p$-divisibility of Picard groups
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2023 at 11:39 | comment | added | Boaz Moerman | @naf Could you turn this into an answer (together with your other comment)? I am not too familiar with spectral sequences, so I have to look into it more, but your argument looks good and solves the important case when $C$ is smooth. Do you also happen to know a way to handle regular curves? | |
| Aug 18, 2023 at 11:34 | comment | added | Boaz Moerman | Thank you for your answer! I had thought that using something using étale group schemes could be useful, but I had missed this argument. | |
| Aug 18, 2023 at 10:53 | comment | added | R. van Dobben de Bruyn | @naf you could turn that into an answer! | |
| Aug 18, 2023 at 4:28 | comment | added | naf | The assumption on $k$ implies that the image of $\mathrm{Gal}(k^{\mathrm{sep}}/k)$ in the automorphisms of $A[\ell]$ has order prime to $\ell$. One can then use the Hoschschild--Serre spectral sequence to show that $H^1(k,A[\ell])$ vanishes. | |
| Aug 18, 2023 at 1:50 | history | undeleted | R. van Dobben de Bruyn | ||
| Aug 18, 2023 at 1:50 | history | edited | R. van Dobben de Bruyn | CC BY-SA 4.0 |
Removed faulty lemma.
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| Aug 18, 2023 at 1:26 | history | deleted | R. van Dobben de Bruyn | via Vote | |
| Aug 18, 2023 at 0:52 | history | edited | R. van Dobben de Bruyn | CC BY-SA 4.0 |
Added a positive result under the 'Kummer theory' assumption.
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| Aug 18, 2023 at 0:14 | history | answered | R. van Dobben de Bruyn | CC BY-SA 4.0 |