On the size of the Jacobians of curves over finite fields
Authors:
Igor Shparlinski
Affiliation:
(1) Department of Computing, Macquarie University, Sydney, NSW, 2109, Australia
Abstract:
Abdract Given a smooth curve of genus g ≥ 1 which admits a smooth projective embedding of dimension m over the ground field of q elements, we obtain the asymptotic formula qg+o(g) for the size of set of the -rational points on its Jacobian in the case when m and q are bounded and g → ∞. We also obtain a similar result for curves of bounded gonality. For example, this applies to the Jacobian of a hyperelliptic curve of genus g → ∞.