Date:
Tue, 29/03/201610:30-11:45
Location:
Ross Building, room 70
Let K be a complete discrete valuation field with finite residue field
of characteristic $p>0$. Let G be the absolute Galois group of
$K$ and for a natural M, let G(M) be the maximal
quotient of G of nilpotent class Then G(M) can be identified with a group obtained from a Lie
Z/p^M-algebra L via (truncated) Campbell-Hausdorff composition law.
Under this identification the ramification subgroups in upper numbering
G(M)^{(v)} correspond to ideals L^{(v)} of L. It will be explained an
explicit construction of L and the ideals L^{(v)}.
The case of fields K of characteristic p was obtained by the author in
1990's (recently refined), the case of fields K of mixed characteristic
requires the assumption that K contains a primitive p^M-th root of unity
(for the case M=1 cf. Number Theory Archive).
of characteristic $p>0$. Let G be the absolute Galois group of
$K$ and for a natural M, let G(M) be the maximal
quotient of G of nilpotent class Then G(M) can be identified with a group obtained from a Lie
Z/p^M-algebra L via (truncated) Campbell-Hausdorff composition law.
Under this identification the ramification subgroups in upper numbering
G(M)^{(v)} correspond to ideals L^{(v)} of L. It will be explained an
explicit construction of L and the ideals L^{(v)}.
The case of fields K of characteristic p was obtained by the author in
1990's (recently refined), the case of fields K of mixed characteristic
requires the assumption that K contains a primitive p^M-th root of unity
(for the case M=1 cf. Number Theory Archive).
