  Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or
ii) the topological fundamental group of a closed connected orientable surface
of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an
elementary and unified proof that every representation $\rho_1: \Gamma \to
\mathbf{GL}_d(\mathbb{F}_p)$ lifts to a representation $\rho_2: \Gamma \to
\mathbf{GL}_d(\mathbb{Z}/p^2)$. [In case i), it is understood these are
continuous.] The actual statement is much stronger: for $r \geq 1$, under
"suitable" assumptions, triangular representations $\rho_r: \Gamma \to
\mathbf{B}_d(\mathbb{Z}/p^r)$ lift to $\rho_{r+1}: \Gamma \to
\mathbf{B}_d(\mathbb{Z}/p^{r+1})$, in the strongest possible step-by-step
sense. Here "suitable" is made precise by the concept of $\textit{Kummer
flag}$. An essential aspect of this work, is to identify the common properties
of groups i) and ii), that suffice to ensure the existence of such lifts.
