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Dec 3, 2016 at 8:49 comment added David Loeffler The specialisation map $H^1(G_{\mathbf{Q}, S}, V \otimes R(\epsilon^{\mathrm{univ}})) \to H^1(G_{\mathbf{Q}, S}, V)$ is injective for every $V$ (because the Iwasawa $H^0$ always vanishes). Does that answer your question?
Dec 2, 2016 at 14:26 comment added Adel BETINA I have another question related to the question above : A small computation tells us that the dimension of $Ext^1_{G_\mathbb{Q}}(1,\psi)$ is one, do you think that the specialization of $H^1(G_{\mathbf{Q}, S}, R(\psi \epsilon^{\mathrm{univ}}))$ to $H^1(G_{\mathbb{Q},S},\psi)$ is not the zero morphism ?
Dec 2, 2016 at 7:43 history edited David Loeffler CC BY-SA 3.0
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Dec 1, 2016 at 22:53 vote accept Adel BETINA
Dec 1, 2016 at 22:32 history answered David Loeffler CC BY-SA 3.0