  In this paper we consider birational properties of ramification in excellent
local rings. We extend earlier results of the author with Olivier Piltant to
show that strong local monomialization is true along a valuation dominating a
defectless extension of two dimensional excellent local rings. We also obtain
general results on the structure of the extension of associated graded rings
along a valuation, and show that the invariants alpha and beta of stable forms
of two dimensional extensions in characteristic p of the author and Olivier
Piltant are not eventually constant.
