The vanishing of anticyclotomic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>μ</mml:mi></mml:math>-invariants for non-ordinary modular forms

ON ANTICYCLOTOMIC ì-INVARIANTS OF MODULAR FORMS

On Anticyclotomic Μ-invariants of Modular Forms

We prove the μ-part of the main conjecture for modular forms along the anticyclotomic Zp-extension of a quadratic imaginary field. Our proof consists of first giving an explicit formula for the algebraic μ-invariant, and then using results of Ribet and Takahashi showing that our formula agrees with Vatsal’s formula for the analytic μ-invariant.

Mazur–tate Elements of Non-ordinary Modular Forms

We establish formulae for the Iwasawa invariants of Mazur–Tate elements of cuspidal eigenforms, generalizing known results in weight 2. Our first theorem deals with forms of “medium” weight, and our second deals with forms of small slope. We give examples illustrating the strange behavior which can occur in the high weight, high slope case.

Ordinary Pseudorepresentations and Modular Forms

In this short note, we observe that the techniques of [WWE15] can be used to provide a new proof of some of the residually reducible modularity lifting results of Skinner and Wiles [SW99]. In these cases, we have found that a deformation ring of ordinary pseudorepresentations is equal to the Eisenstein local component of a Hida Hecke algebra. We also show that Vandiver’s conjecture implies Shar...

Modular Forms and Projective Invariants