Talk:Tate module

Notation question

I'm not sure what to make of the equation $z(a_{n})_{n}=((z\mod {p^{n}})a_{n})_{n}$, though I believe I understand the Z_p action on the Tate module.

Shouldn't it be $z(a)_{n}=((z\mod {p^{n}})a_{n})$? That is, we define the n-th approximation of z acting on a by taking the (z mod p^n)-th multiple of the n-th approximation of a. Is there any meaning to the extra subscripts n in the current equation? 140.114.81.55 (talk) 05:53, 24 August 2010 (UTC)

Typically, the notation $(a_{n})_{n}$ is a shortening of $(a_{n})_{n\in I}$ (where I here is the index set of positive integers), i.e. the extra n is there to indicate that we are dealing with a tuple. RobHar (talk) 15:06, 24 August 2010 (UTC)

OK; I get it now. Thanks! 140.114.81.55 (talk) 04:54, 25 August 2010 (UTC)