7
$\begingroup$

On page 174 of both copies I can access of Mumford's book "Lectures on Curves on an Algebraic Surface" there is a printing omission (like this one).

LEMMA 2: Let $A$ be a complete $p$-adic ring where $p$ is not a zero-divisor, such that $A/p$ is perfect. Then there is a 1-1 correspondence between members of $A$ and sequences $(\xi_0,\xi_1,\ldots)$ of elements of $A/p$, given by...

Who can supply the missing text?

$\endgroup$
10
$\begingroup$

In the Russian edition it is $$(\xi_0,\xi_1,\xi_2,\dots)\leftrightarrow f(\xi_0)+pf(\xi_1)+p^2f(\xi_2)+\dots$$ where $f$ is the Teichmuller map.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.