Representation of Witt Vectors by Formal Power Series and its Applications

Abstract

K$ of characteristic $p$ by the matrix equation of the type $X^{p}=MX,$ $MeGL.(K)$ . We define in \S 1 an isomorphism $f_{u}$ of the additive group $W_{\infty}(K)$ of Witt vectors into the multiplicative 1- unit group of the formal power series ring $K[[t]]:f_{u}(\alpha+\alpha')=f_{u}(\alpha)\cdot f_{u}(\alpha^{\prime}).*)$