Timeline for Non-abelian group from affine hermitian curve
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2013 at 8:01 | vote | accept | Hiren | ||
| Dec 14, 2013 at 7:59 | comment | added | Hiren | Thanks for your answer. I found the group law as follows: let t(a,b) be the tangent line through the point (a,b). Then t(a,b) = y-a^qx +b^q. Check that: t(a,b)^q + t(a,b) = (x_a)^{q+1} where x_a = x-a. This equation is just the same as that defining the Hermitian curve with t(a,b) replacing y and x_a replacing x. Now let T(c,d) be the tangent line (in terms of t(a,b) and x_a) to this curve at the point (c,d). Then T(c,d) = t(a,b) - c^qx_a + d^q and one checks that T(c,d) equals t(a+c,b+d+ca^q). So, from the points (a,b) and (c,d) we 'get' the point (a+c,b+d+ca^q). This gives a group. | |
| Dec 13, 2013 at 23:54 | history | answered | Michael Zieve | CC BY-SA 3.0 |