For smooth projective curves over global fields, the mod-l kernel of the boundary map is governed by local reduction data and the Galois coinvariants J[l]_{G_F}.
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A Hasse principle for the higher Chow groups of curves over a global field
For smooth projective curves over global fields, the mod-l kernel of the boundary map is governed by local reduction data and the Galois coinvariants J[l]_{G_F}.