Let $A$ be a complete discrete valuation ring with fraction field $K$ and residue field $k$, and let $T$ be a finite commutative $A$-algebra acting on a finite free $A$-module $M$. If a system of eigenvalues $\lambda:T\to k$ occurs in $M\otimes_A k$, then after possibly replacing $A$ by the ring of integers of a finite extension of $K$ there is an eigenvector in characteristic zero whose eigenvalues lift the given residual system.