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Bisection for genus 2 curves in odd characteristic. (English) Zbl 1213.11130

Summary: We show how to invert the multiplication-by-2 map in Jacobians of genus 2 curves \(\text{C}\) over finite fields \(\mathbb F_q\) of odd characteristic. For any divisor \(D\in \text{Jac}(\text{C})(\mathbb F_q)\) we provide a method to construct the coordinates of all divisors \(D^\prime\in \text{Jac}(\text{C})(\mathbb F_q)\) such that \(2D^\prime=D\).

MSC:

11G20 Curves over finite and local fields
14H40 Jacobians, Prym varieties
14H25 Arithmetic ground fields for curves
14G15 Finite ground fields in algebraic geometry

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References:

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