Yoshifumi Tsuchimoto
There is diverse deep theories on elliptic curves.
Let
be a field of characteristic
.
We consider a curve
in
of the following type:
(The equation, of course, is written in terms of inhomogeneous coordinates. In homogeneous coordinates, the equation is rewritten as:
Such a curve is called an elliptic curve. It is well known (but we do not prove in this lecture) that
We would like to calculate congruent zeta function of
.
For the moment, we shall be content to prove: