Timeline for Jacobians defined over smaller fields
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 7, 2012 at 16:11 | comment | added | user27056 | @inkspot: Thanks for correcting my mistaken memory. So the genus-1 case (for which compatibility with the p.p. is automatic, due to its uniqueness in such cases) is more special for this question than I had been expecting. | |
| Oct 7, 2012 at 9:50 | comment | added | inkspot | @xbnv: I meant hyperelliptic. In this case the curve and its Jacobian have the same automorphism group and Galois descent data transfer both ways. In the non-hyperelliptic case the Jacobian has more automorphisms (the $-1$); you can then twist the Jacobian by this $-1$ and, as it were, "lose the curve". The reference to Serre is to arXiv 0104247, his paper with Lauter. | |
| Oct 7, 2012 at 9:22 | comment | added | user27056 | @inkspot: I deleted my previous comment. In your new final sentence, I think you meant "not hyperelliptic" (since the "ppav" functor on non-hyperelliptic curves is fully faithful and so Galois descent data transfers both ways). | |
| Oct 7, 2012 at 9:06 | comment | added | inkspot | @xbnv: my edit crossed with your comment. I hope things are clearer now (I forgot the quadratic twist). | |
| Oct 7, 2012 at 9:05 | history | edited | inkspot | CC BY-SA 3.0 |
Corrected to refer to Serre.
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| Oct 7, 2012 at 8:44 | history | answered | inkspot | CC BY-SA 3.0 |