For wildly ramified K/k with G=(Z/pZ)^2 the elements (σ1-1)^i(σ2-1)^j act on the valuation filtration in a computable way and yield good bases when ramification jumps are distinct modulo p^2.
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Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$
For wildly ramified K/k with G=(Z/pZ)^2 the elements (σ1-1)^i(σ2-1)^j act on the valuation filtration in a computable way and yield good bases when ramification jumps are distinct modulo p^2.