Timeline for Smooth complete intersections and sharpness of the Chevalley-Warning theorem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2015 at 6:48 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Oct 6, 2015 at 19:12 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Oct 6, 2015 at 19:11 | comment | added | Daniel Loughran | Yes you are right, thanks for pointing this out. The problem was I started with $x_0$, instead of $x_1$. I will change my answer accordingly. | |
| Oct 6, 2015 at 15:13 | comment | added | Jason Starr | I see what happened. You probably wanted to consider the zero locus of $x_0^{q-1} + \dots + x_{q-2}^{q-1}$ in $\mathbb{P}^{q-2}$. If $q$ is prime, this polynomial has zero solutions in $\mathbb{F}_q$, and zero is not congruent to one. | |
| Oct 6, 2015 at 15:02 | comment | added | Jason Starr | Could you please double-check this? If $q$ is an odd prime, I compute that the number of solutions is $(q-1)^{q-1}$, which is congruent to $1$ modulo $q$ (possibly making a mistake, but I did get this also for $q=4$). | |
| Oct 6, 2015 at 14:47 | history | answered | Daniel Loughran | CC BY-SA 3.0 |