Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $(A_n)<$ be a projective and inductive system of $\mathbb{Z}/p^n$-modules.

Is then $\operatorname{Hom}{(\projlim A_n, \mathbb{Z}_p)}$ isomorphic to $\operatorname{Hom}(\operatorname{Div}(\injlim A_n), \mathbb{Q}_p/\mathbb{Z}_p)$, resp. under which additional (finiteness?) assumptions does this hold? $\operatorname{Div}$ denotes the maximal divisible subgroup.

share|cite|improve this question
Are you saying to consider both the limit and colimit of the same diagram? So for example for the diagram of finite quotients of $\mathbb{Z}_p$ you would have $\mathbb{Z}_p$ as the limit and $0$ as the colimit? Your claim does not hold in this case. – jspecter Sep 8 '11 at 6:39
$(A_n)$ comes from a $p$-adic sheaf. – user5262 Sep 8 '11 at 6:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.