Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices

We study the ramification groups of finite Galois extensions L/K of a complete discrete valuation field K of equal characteristic p>0 with perfect residue field and Galois group isomorphic to the group of unitriangular matrices UTn(Fp) over Fp. We show that the upper ramification breaks can be expressed as a linear function of the valuation of the entries of a matrix directly constructed from the coefficients of a defining equation of the extension. This allows us to compute the ramification groups without using any elements of L−K.