The class group pairing and $p$-descent on elliptic curves
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en
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Proceedings of the London Mathematical Society. 2013, vol. 106, n° 2, p. 345-374
London Mathematical Society
Resumen en inglés
We give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the ...Leer más >
We give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the resulting Selmer group with the logarithmic class group of the base. These constructions are explicit and suitable for computer experimentation. From a conceptual point of view, the questions that arise here are analogues of "visibility" questions in the sense of Cremona and Mazur.< Leer menos
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