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)