2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225582We verify a special case of a conjecture of G. Carlsson that describes the $ł$-adic $K$-theory of a field $F$ of characteristic prime to $ł$ in terms of the representation theory of the absolute Galois group $G_F$. This conjecture is known to hold in two cases; in this article we examine the second case, in which the field in question is the field of Laurent series over a finite field $\FF_{p}((x))$.Added acknowledgmentsK-Theory and HomologyAlgebraic Topology19D50 (Primary); 55P99 (Secondary)text