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.
p-adic families of cohomological modular forms for indefinite quaternion algebras and the Jacquet-Langlands correspondence / M. Greenberg, M.A. Seveso. - In: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. - ISSN 0008-414X. - 68:5(2016), pp. 961-998. [10.4153/CJM-2015-062-x]
p-adic families of cohomological modular forms for indefinite quaternion algebras and the Jacquet-Langlands correspondence
M.A. SevesoUltimo
2016
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 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.File | Dimensione | Formato | |
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