Timeline for Effective Lang-Weil bounds for del Pezzo surfaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2018 at 12:35 | answer | added | Daniel Loughran | timeline score: 7 | |
| Aug 18, 2013 at 15:02 | comment | added | Felipe Voloch | Like I said, Manin's book. Theorem 27.1 and corollary 27.1.1. | |
| Aug 18, 2013 at 13:43 | comment | added | Casaubon | Dear Ulrich, is there any reference for that result (besides reading the proof ...)? Thanks! | |
| Aug 18, 2013 at 12:56 | comment | added | naf | In general, one gets much better bounds for smooth projective vareties using Deligne's proof of the Weil conjecture. For a del Pezzo surface $X$ you get that the error term is bounded by $bq + 1$ where $b$ is the second Betti number of $X$, which is the number of points of $\mathbb{P}^2$ blown up to get $X$ (over an algebraic closure of $\mathbb{F}_q)$ plus $1$ (so between $1$ and $9$). | |
| Aug 18, 2013 at 12:48 | comment | added | Felipe Voloch | Del Pezzo surfaces are rational and you can work out their zeta function explicitly. This should be in Manin's book on cubic surfaces. | |
| Aug 18, 2013 at 12:24 | history | asked | Casaubon | CC BY-SA 3.0 |