Let $R$ be a ring that is $p$-adically complete for a prime $p$ and let $W(R)$ denote the ring of $p$-typical Witt vectors. Is it true that $W(R)$ is $p$-adically complete? (A ring $A$ is $p$-adically complete if the map $A \rightarrow \varprojlim(A/p^nA)$ is bijective.) A reference that contains a proof or a counterexample would suffice.


I am familiar with the case when $R$ is a perfect $\mathbb{F}\_p$-algebra and am interested in the general case.



$p$-adic completeness of the ring of Witt vectors
The answer is yes. A reference is $\S1$, proposition 3 of *"The display of a formal $p$-divisible group"* by Thomas Zink, published in Asterisque no. 278. 
Here is the address of the paper on Zink's website... 


<https://www.math.uni-bielefeld.de/~zink/display.pdf>


