On anticyclotomic mu-invariants of modular forms
Number Theory
2019-02-20 v1
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).
Keywords
Cite
@article{arxiv.math/0610694,
title = {On anticyclotomic mu-invariants of modular forms},
author = {Robert Pollack and Tom Weston},
journal= {arXiv preprint arXiv:math/0610694},
year = {2019}
}