Ramification filtration via deformations

Abstract

Let be a field of formal Laurent series with coefficients in a finite field of characteristic , the maximal quotient of the Galois group of of period and nilpotency class and the filtration by ramification subgroups in the upper numbering. Let be the identification of nilpotent Artin-Schreier theory: here is the group obtained from a suitable profinite Lie -algebra via the Campbell-Hausdorff composition law. We develop a new technique for describing the ideals such that and constructing their generators explicitly. Given , we construct an epimorphism of Lie algebras and an action of the formal group of order , , , on . Suppose , where , and is the ideal of generated by the elements of . The main result in the paper states that . In the last sections we relate this result to the explicit construction of generators of obtained previously by the author, develop a more efficient version of it and apply it to recover the whole ramification filtration of from the set of its jumps. Bibliography: 13 titles.