Timeline for Computing the group structure of $J(\mathbb{F}_q)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 28, 2021 at 10:26 | comment | added | Aurel | If you want a polynomial time algorithm, this is open: we don't even know how to compute the cardinality of this group in polynomial time (if the genus and the characteristic both vary). | |
| May 28, 2021 at 10:23 | comment | added | Aurel | Do you want any algorithm or an efficient algorithm? If the former, the only problem is how to perform elementary operations in $J(k)$ (since this is a finite group); this can be done for instance using Riemann-Roch spaces, say using Makdisi's algorithms arxiv.org/abs/math.NT/0105182 | |
| May 28, 2021 at 8:27 | comment | added | Gro-Tsen | This can be broken down into two questions: ①how to compute $J$, as an algebraic (abelian) variety (i.e., write down equations for it and for its addition law) in function of $X$, and ②given $J$, how to compute its points over a finite field or its torsion points over a number field. It's not entirely clear what interests you. This question asks about part ①, and provides some references. | |
| May 28, 2021 at 7:49 | history | edited | k.j. | CC BY-SA 4.0 |
added 171 characters in body
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| May 28, 2021 at 7:20 | history | asked | k.j. | CC BY-SA 4.0 |