Control theorems for ordinary 2-adic families of modular forms

Ghate, Eknath and VG Narasimha Kumar, C H (2013) Control theorems for ordinary 2-adic families of modular forms. Automorphic representations and l-functions.

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Abstract

We prove a control theorem for Hida’s ordinary Hecke algebra for the primep= 2,thereby establishing a uniqueness result for ordinary 2-adic families of cusp forms. As a conse-quence we show that the possibly finitely many exceptions that arise, in showing that the localGalois representations attached to the arithmetic members of a non-CM ordinary 2-adic familyof cuspidal eigenforms are all non-split, contain no CM forms.

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