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When i = 1, an affi rmative an swe r to eithe r one of the s e que stions woul d imply a p o s itive solution f o r the "c ong ruenc e sub ­ g roup pr oblem" on abelian va rietie s , d. [24], §3 . ) -. ] Remark The concept of a n l-adic representation can be generalized by replacing the prime 1 by a place }.. of a E. -adic representation is then a continuous homomorphism Gal(K /K} s � A where V is a finite-dimensional vector Aut(V}, spa ce over the local field E}... , can be defined in a way similar to the 1-adic case.

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