On Jacquet-Langlands isogeny over function fields

Mathematics – Number Theory

Scientific paper

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29 pages

Scientific paper

We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic
Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of
$\mathcal{D}$-elliptic sheaves. The kernel of the isogeny is a subgroup of the
cuspidal divisor group constructed by examining the canonical maps from the
cuspidal divisor group into the component groups.

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