Let Γ 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 µ p 2 ⊂ F . We give an elementary and unified proof that every representation ρ 1 : Γ -→ GL d (Fp) lifts to a representation ρ 2 : Γ -→ GL d (Z/p 2 ). [In case i), it is understood these are continuous.] The actual statement is much stronger: for all r ≥ 1, under "suitable" assumptions, strictly upper triangular representations ρr : Γ -→ U d (Z/p r ) lift to ρ r+1 : Γ -→ U d (Z/p r+1 ), in the strongest possible stepby-step sense. Here "suitable" is made precise by the concept of 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.