Abstract
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.
Subject
Algebra and Number Theory
Cited by
2 articles.
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1. Ramification filtration and differential forms;Известия Российской академии наук. Серия математическая;2023
2. Ramification filtration and differential forms;Izvestiya: Mathematics;2023