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  • But the question of whether the image of rho must be open in GSp_2g(Z_l) whenever no ???obvious??? geometric obstruction forbids it is difficult, and still not completely understood. (I believe it???s still unknown when g is a multiple of 4????) One thing we do know in general, though, is that when X is the generic curve of genus g (that is, the universal curve over the function field Q(M_g) of M_
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