Open questions and recent developments in Iwasawa theory

Open questions and recent developments in Iwasawa theory
in honor of Ralph Greenberg's 60th birthday
June 2005

p-adic families of modular forms on definite quaternion algebras and arithmetic applications


Massimo Bertolini

University of Milan

Abstract

Building on ideas of Greenberg and Stevens, we describe certain exceptional zero formulae for Hida p-adic L-functions arising from modular symbols or modular forms on definite quaternion algebras. In some cases, these results lead to the construction of rational points on modular abelian varieties.