For Tate twists Z_p(2), which is defined by the projective limit of \mu_{p^m}(2) over all m>0, I would like to calculate H^1(Q_p, Z_p(2)).

I guess this is zero, but cannot prove it. Is it possible to calculate and prove H^1(Q_p, \mu_{p^m}(2)) = 0 for each m> 0?

Just teach me, please.

Pierre MATSUMI