On anticyclotomic mu-invariants of modular forms

Abstract

Let f be a modular form of weight 2 and trivial character. Fix also an imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic Zp-extension of K. In particular, we verify the mu-part of the main conjecture in this context. The proof of this result is based on an analysis of congruences of modular forms, leading to a conjectural quantitative version of level-lowering (which we verify in the case that Mazur's principle applies).

References in corpus (1)

• Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields

Cited by in corpus (21)

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• Iwasawa Main Conjecture for Supersingular Elliptic Curves and BSD conjecture
• A proof of Perrin-Riou's Heegner point main conjecture
• Hirzebruch-Zagier cycles and twisted triple product Selmer groups
• On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes
• On the dihedral main conjectures of Iwasawa theory for Hilbert modular eigenforms
• Rank parity for congruent supersingular elliptic curves
• Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication
• Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
• Quantitative level lowering for Galois representations
• On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights
• Indivisibility of Heegner cycles over Shimura curves and Selmer groups
• Special Values of Anticyclotomic L-functions Modulo λ
• Structure of fine Selmer groups over ${\mathbb{Z}}_p$-extensions
• Anticyclotomic $\mu$-invariants of residually reducible Galois Representations
• Iwasawa Invariants for elliptic curves over ${\mathbb{Z}}_p$-extensions and Kida's Formula
• On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in ${\mathbb{Z}}_p$-extensions
• On the non-vanishing of generalized Kato classes for elliptic curves of rank $2$
• Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory
• Iwasawa Theory of Hilbert modular forms for anticyclotomic extension
• The vanishing of anticyclotomic $\mu$-invariants for non-ordinary modular forms