Abstract
Let M be a two-dimensional motive which is pure of weight w over a number field K and let (φl: GK →Aut(Hl(M) ))l be the system of the l-adic realizations. Choose GK-invariant ℤl -lattices Tl of Hl(M) and let (φl:GK →GL (Tl))lbe the corresponding system of integral representations. Then either for almost all primes φl (GK) consist of all the elements of GL(Tl) with determinant in (ℤl*)−w or the system (φl) is associated to algebraic Hecke characters. We also can prove an adelic version of our results.
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