P–adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the Jacquet–Langlands Correspondence. (1st October 2016) - Greenberg, Matthew; Seveso, Marco
Abstract: We use the method of Ash and Stevens to prove the existence of small slope p -adic families of cohomological modular forms for an indefinite quaternion algebra B . We prove that the Jacquet–Langlands correspondence relating modular forms on GL_2/Q and cohomomological modular forms for B is compatible with the formation of p -adic families. This result is an analogue of a theorem of Chenevier concerning definite quaternion algebras.