Question about witt vector of some ring - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T14:21:53Z http://mathoverflow.net/feeds/question/104753 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104753/question-about-witt-vector-of-some-ring Question about witt vector of some ring TOM 2012-08-15T09:55:57Z 2012-08-15T09:55:57Z <p>Suppose $R=Z_p[t]$ , and $\hat{R}$ its p-adic completion, suppose we have Endormorphism $\Phi$ of $\hat{R}$, whose redution mop p is just the absolute Frobenius of $\hat{R}/p\hat{R}$. And $R_{\infty}=dir.lim\hat{R}$, the direct limit is over copies of $\hat{R}$ indexed by the natrual numbers, and the transition maps are given by $\Phi$ mapping from one copy to the next. If we denote $\hat{R_{\infty}}$ the p-adic completion of $R_{\infty}$. Then is it true that $\hat{R_{\infty}}$ isomorphic to $W(\hat{R_{\infty}}/p\hat{R_{\infty}})$, the Witt-vectors over $\hat{R_{\infty}}/p\hat{R_{\infty}}$ and why it is true? Thank you!</p>