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

Abstract

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.

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

References in corpus (2)

• On anticyclotomic mu-invariants of modular forms
• On the dihedral Euler characteristics of Selmer groups of abelian varieties

Cited by in corpus (5)

• Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication
• Rankin-Selberg L-functions in cyclotomic towers, III
• On the dihedral Euler characteristics of Selmer groups of abelian varieties
• An anticyclotomic Mazur-Tate conjecture for modular forms
• On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights