Rational Torsion on Jacobians of Curves of Genus at least two
نویسنده
چکیده
with A,B ∈ k. Then the rational point that comes with the curve is O = (0: 1 : 0), in the projective model Y Z = X +AXZ +BZ. There is a group law on an elliptic curve, given as follows. Let P,Q be points on the curve. Draw the unique line through P and Q (the tangent at P if they are equal) and find the unique third point of intersection, R, with the curve; this exists by Bézout’s theorem. Now draw the vertical line through R and define P +Q to be the other intersection point of this line with the curve. By its construction this group law is commutative.
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