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  1. Abstract We prove an integral {R=\mathbf{T}} theorem for odd two-dimensional p -adic representations of {G_{\mathbf{Q}}} which are unramified at p ,extending results of [5]to the non-minimal case. We prove, for any p , the existenceof Katz modular forms modulo p of weight one which do not lift tocharacteristic zero. 
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