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Bipartite Euler systems
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October 17, 2006
Abstract
If E is an elliptic curve over ℚ and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic ℤp-extension of K. The main conjecture takes different forms depending on the sign of the functional equation of L(E/K, s). In the present work we combine ideas of Bertolini and Darmon with those of Mazur and Rubin to shown that the main conjecture, regardless of the sign of the functional equation, can be reduced to proving the nonvanishing of sufficiently many p-adic L-functions attached to a family of congruent modular forms.
Received: 2004-09-14
Revised: 2005-05-13
Published Online: 2006-10-17
Published in Print: 2006-08-01
© Walter de Gruyter
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Articles in the same Issue
- Bipartite Euler systems
- Modular curves and Ramanujan's continued fraction
- Global anti-self-dual Yang-Mills fields in split signature and their scattering
- Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles
- Definable sets in algebraically closed valued fields: elimination of imaginaries
Articles in the same Issue
- Bipartite Euler systems
- Modular curves and Ramanujan's continued fraction
- Global anti-self-dual Yang-Mills fields in split signature and their scattering
- Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles
- Definable sets in algebraically closed valued fields: elimination of imaginaries
