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2-Descent on the Jacobians of Hyperelliptic Curves

✍ Scribed by E.F. Schaefer

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 470 KB
Volume: 51
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1044

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✦ Synopsis

Let (J) be the Jacobian of the hyperelliptic curve (Y^{2}=f\left(X^{2}\right)) over a field (K) of characteristic 0 , where (f) has odd degree. We shall present an embedding of the group (J(K) / 2 J(K)) into the group (L^{* / L^{* 2}}) where (L=K[T] / f(T)). Since this embedding is derived from the coboundary map of Galois cohomology, it can be used to compute a 2-descent for the Jacobian. We will use this embedding to compute (J(\mathbf{Q}) 2 J(\mathbf{Q})) for a rank-2 Jacobian of a hyperelliptic curve of genus 3. Academic Press. Inc

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