Timeline for Relation between divisibility problem of Shafarevich group and group structure of $Ш(E/K)$
Current License: CC BY-SA 4.0
5 events
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| Mar 3, 2023 at 11:07 | comment | added | Chris Wuthrich | I also think that Cassels' question of the divisibility in the Weil-Châtelet group is not really about the group structure of Sha as an abelian group (which I consider a well-posed problem). The opposite would: If one could prove that elements in Sha are not divisible in the ambient group, then the $p$-primary part of Sha would be finite. Therefore, the divisibility Cassels conjectures sort of says it is hard to prove that Sha is finite. | |
| Mar 3, 2023 at 6:17 | comment | added | Wojowu | "group structure" is not a well-posed problem. The divisibility for large $p$ follows from the (conjectured) finiteness of Sha, simply because every finite abelian group is divisible by all primes not dividing its order. For primes dividing the order, it's hard to tell how the two are related, since Cassels' problem then asks about existence of certain classes outside Sha itself. | |
| Mar 3, 2023 at 5:58 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo
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| Mar 3, 2023 at 5:04 | history | edited | Duality | CC BY-SA 4.0 |
added 6 characters in body
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| Mar 3, 2023 at 4:41 | history | asked | Duality | CC BY-SA 4.0 |