On p-adic Families of Automorphic Forms

Abstract

Coleman and Mazur have constructed "eigencurves", geometric objects parametrising certain overconvergent p-adic modular forms. We formulate definitions of overconvergent p-adic automorphic forms for two more classes of reductive groups — firstly for GLI over a number field, and secondly for D x , D a definite quaternion algebra over the rationals. We give several reasons why we believe the objects we construct to be the correct analogue of an overconvergent p-adic modular form in this setting.