Timeline for Counting abelian varieties over finite fields in a given isogeny class
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2015 at 15:38 | comment | added | Felipe Voloch | For $g=2$ there are papers of Howe, Maisner, Nart, Ritzenthaler which may help. | |
| Sep 12, 2015 at 15:21 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Sep 12, 2015 at 15:19 | comment | added | Will Sawin | @FelipeVoloch Thanks for the reference! Unfortunately I think the polarization is crucial because that's where the unit group will come in - the class group is not a nice count because you should really divide by the order of the automorphism group, which is infinite. I think that's related to why there isn't as nice an analytic formula as in the imaginary quadratic case - the regulator appears in the class number formula. | |
| Sep 11, 2015 at 22:32 | comment | added | Felipe Voloch | It's a (Kronecker) class number. For elliptic curves, this is (of course) in Deuring. Good references are Schoof J. Comb. Th. 1987, for elliptic curves and Waterhouse, Ann. Sci ENS 1969, in general (but maybe the polarization is an issue in dim > 1). | |
| Sep 11, 2015 at 21:31 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Sep 11, 2015 at 21:27 | comment | added | Vesselin Dimitrov | Is there a missing square root, as in $\sqrt{q}$? | |
| Sep 11, 2015 at 21:15 | history | asked | Will Sawin | CC BY-SA 3.0 |