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Descent on certain Shimura curves

✍ Scribed by Alexei Skorobogatov; Andrei Yafaev

Publisher: The Hebrew University Magnes Press
Year: 2004
Tongue: English
Weight: 612 KB
Volume: 140
Category: Article
ISSN: 0021-2172
DOI: 10.1007/bf02786638

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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 der