Ramification filtration via deformations

Abstract Let be a field of formal Laurent series with coefficients in finite characteristic $p$?> , G_{ the maximal quotient Galois group period and nilpotency class $ $\{\mathscr G_{ filtration by ramification subgroups upper numbering. G_{ identification nilpotent Artin-Schreier theory: here $G(\mathscr is obtained from suitable profinite Lie $\mathbb{F}_p$?> -algebra L$?> via Campbell-Hausdorff composition law. We develop new technique for describing ideals L^{(v)}$?> such that L^{(v)})=\mathscr G_{ constructing their generators explicitly. Given $v_0\geqslant 1$?> we construct an epimorphism algebras $\overline\eta^{\unicode{8224}}\colon \mathscr L\to \overline{\mathscr L}^{\unicode{8224}}$?> action $\Omega_U$?> order $\alpha_p=\operatorname{Spec}\mathbb{F}_p[U]$?> $U^p=0$?> on $\overline{\mathscr . Suppose $d\Omega_U=B^{\unicode{8224}}U$?> where $B^{\unicode{8224}}\in\operatorname{Diff}\overline{\mathscr L}^{\unicode{8224}}[v_0]$?> ideal generated elements $B^{\unicode{8224}}(\overline{\mathscr L}^{\unicode{8224}})$?> The main result paper states L^{(v_0)}=(\overline\eta^{\unicode{8224}})^{-1}\overline{\mathscr In last sections relate this to explicit construction L^{(v_0)}$?> previously author, more efficient version it apply recover whole set its jumps. Bibliography: 13 titles.