 
Summary: Towards arithmetical description of the Galois group of a local field.
Victor Abrashkin (Durham University)
Let K be a complete discreet valuation field with residue field of characteristic
p. Let #K be the absolute Galois group of K and let #K (p) be the Galois group of
the maximal pextension of K. What we can say about its structure? The known
cases are:
 if char K = p then #K (p) is propfree;
 if char K = 0 and k is finite (i.e. K is onedimensional), then
 if # p /
# K, then #K (p) is propfree;
 if # p # K, then #K (p) is the Demushkin group.
What we can say if K is an Ndimensional local field? (This means that k is
an (N  1)dimensional local field.) Notice that ``1dimensional'' methods can't be
directly generalized to study the higher dimensional case.
Alternative ``1dimensional'' approach: characteristic p case.
Assume for simplicity that K = F p ((t)). Then the ArtinSchreier theory gives
an explicit description of the group #K /# p
K C 2 (#K ), where C 2 (#K ) is the closed
subgroup generated by commutators of order # 2. This group appears as the Galois
group of the extension K({T a  (a, p) = 1 or a = 0})/K, where T p
