Teitelbaum's exceptional zero conjecture in the anticyclotomic setting

Teitelbaum’s exceptional zero conjecture in the anticyclotomic setting

In [Tei], Teitelbaum formulates a conjecture relating first derivatives of the Mazur– Swinnerton-Dyer p-adic L-functions attached to a modular forms of even weight k ≥ 2 to certain L-invariants arising from Shimura curve parametrisations. 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 ...

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...

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

Proof of an Exceptional Zero Conjecture for Elliptic Curves over Function Fields

Based on the analogy between number fields and function fields of one variable over finite fields, we formulate and prove an analogue of the exceptional zero conjecture of Mazur, Tate and Teitelbaum for elliptic curves defined over function fields. The proof uses modular parametrization by Drinfeld modular curves and the theory of non-archimedean integration. As an application we prove a refine...