Journal of the Ramanujan Mathematical Society

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Non-Triviality of Families of Heegner Points and Ranks of Selmer Groups over Anti Cyclotomic Towers


Affiliations
1 Universita di Pavia, Dipartimento di Matematica Via Abbiategrasso 215 27100 Pavia, Italy
2 McGill University, Mathematics Department, 805 Sherbrooke Street West Montreal QC H3A 2K6, Canada
     

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Let E/Q be a modular elliptic curve of conductor N and let K be an imaginary quadratic field of discriminant prime to N. Assume that E is semistable at all the prime divisors of N which are inert in K, and that the Hasse-Weil L-function L(E/K, s) vanishes to even order at s = 1.
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  • Non-Triviality of Families of Heegner Points and Ranks of Selmer Groups over Anti Cyclotomic Towers

Abstract Views: 249  |  PDF Views: 0

Authors

Massimo Bertolini
Universita di Pavia, Dipartimento di Matematica Via Abbiategrasso 215 27100 Pavia, Italy
Henri Darmon
McGill University, Mathematics Department, 805 Sherbrooke Street West Montreal QC H3A 2K6, Canada

Abstract


Let E/Q be a modular elliptic curve of conductor N and let K be an imaginary quadratic field of discriminant prime to N. Assume that E is semistable at all the prime divisors of N which are inert in K, and that the Hasse-Weil L-function L(E/K, s) vanishes to even order at s = 1.