Explicit quadratic Chabauty over number fields

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作者
Jennifer S. Balakrishnan
Amnon Besser
Francesca Bianchi
J. Steffen Müller
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[1] Boston University,Department of Mathematics and Statistics
[2] Ben-Gurion University of the Negev,Department of Mathematics
[3] University of Groningen,Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence
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摘要
We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combining equations coming from Siksek’s extension of classical Chabauty with equations defined in terms of p-adic heights attached to independent continuous idele class characters. We give several examples to show the practicality of our methods.
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页码:185 / 232
页数:47
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