Teitelbaum’s exceptional zero conjecture in the anticyclotomic setting

TEITELBAUM ’ S EXCEPTIONAL ZERO CONJECTURE IN THE ANTICYCLOTOMIC SETTING By MASSIMO BERTOLINI

Teitelbaum formulated a conjecture relating first derivatives of the Mazur-SwinnertonDyer p-adic L-functions attached to modular forms of even weight k ≥ 2 to certain L-invariants arising from Shimura curve parametrizations. This article formulates an analogue of Teitelbaum’s conjecture in which the cyclotomic Zp extension of Q is replaced by the anticyclotomic Zp-extension of an imaginary quad...

The anticyclotomic Main Conjecture for elliptic curves at supersingular primes

The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Zp-extension of an imaginary quadratic field K was studied in [BD2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by...

Families of automorphic forms on definite quaternion algebras and Teitelbaum’s conjecture

Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions

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.