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.
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Buzzard, K. (2004). On p-adic Families of Automorphic Forms. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_2
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_2
Publisher Name: Birkhäuser, Basel
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