p-adic families of cohomological modular forms for indefinite quaternion algebras and the Jacquet-Langlands correspondence

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 GL2/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.