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On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms

Published online by Cambridge University Press:  20 November 2018

Jeanine Van Order
Jeanine Van Order*
Affiliation:
Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland, e-mail: jeanine.vanorder@epfl.ch
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Abstract

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We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini–Darmon, Longo, Nekovar, Pollack–Weston, and others. The construction has direct applications to Iwasawa's main conjectures. For instance, it implies in many cases one divisibility of the associated dihedral or anticyclotomic main conjecture, at the same time reducing the other divisibility to a certain nonvanishing criterion for the associated $p$-adic $L$-functions. It also has applications to cyclotomic main conjectures for Hilbert modular forms over $\text{CM}$ fields via the technique of Skinner and Urban.

Keywords

11G1011G1811G40Iwasawa theoryHilbert modular formsabelian varieties
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 2 , 01 April 2013 , pp. 403 - 466
Copyright
Copyright © Canadian Mathematical Society 2013

References

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