On the dihedral main conjectures of Iwasawa theory for Hilbert modular eigenforms

Details On the dihedral main conjectures of Iwasawa theory for Hilbert modular eigenforms On the dihedral main conjectures of Iwasawa theory for Hilbert modular eigenforms

2011-12-16

arxiv.org/abs/1112.3823v3

Mathematics

Number Theory

58 pages, absolute final version with very minor edits, to appear in the Canadian Journal of Mathematics

Scientific paper

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 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 CM fields via the technique of Skinner and Urban.

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