Timeline for Zeta function of Abelian variety over finite field
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18, 2017 at 14:09 | comment | added | Noam D. Elkies | The curve case is interesting, but must be well-known enough that there's no need to duplicate it here . . . | |
| Oct 18, 2017 at 13:26 | comment | added | user19475 | Please don't delete your answer, the curve case is also interesting! | |
| Oct 18, 2017 at 13:10 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Acknowledge error
|
| Oct 18, 2017 at 13:09 | comment | added | Noam D. Elkies | Sorry, I was answering the wrong question . . . Let me think again. | |
| Oct 18, 2017 at 3:33 | comment | added | R. van Dobben de Bruyn | I think that the formula $\sigma_n = q^n + 1 - |A(\mathbb F_{q^n})|$ only works for curves. For an abelian variety $A$, the count $|A(\mathbb F_{q^n})|$ looks like $1 - \sum_i \lambda_i^n + \sum_{i < j} (\lambda_i\lambda_j)^n - \ldots + q^{gn}$. It would be interesting to try to put that into a similar generating function; it seems that this would be much harder. | |
| Oct 18, 2017 at 3:14 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |