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We give a characteristic free proof of the main result of our previous paper(math.AC/0509697) concerning toroidalization of generating sequences ofvaluations in dimension two function fields. We show that when an extension oftwo dimensional algebraic regular local rings $R\subset S$ satisfies theconclusions of the Strong Monomialization theorem of Cutkosky and Piltant, themap between generating sequences in $R$ and $S$ has a toroidal structure.

Toroidalization of generating sequences in dimension two function fields of positive characteristic