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RAMIFICATION THEORY FOR HIGHER DIMENSIONAL LOCAL FIELDS
 

Summary: XXXX
RAMIFICATION THEORY FOR HIGHER
DIMENSIONAL LOCAL FIELDS
Victor Abrashkin
To 60th birthday of A.N.Parshin.
Abstract. The paper contains a construction of ramification theory for higher di­
mensional local fields K provided with additional structure given by an increasing
sequence of their ``subfields of i­dimensional constants'', where 0 # i # n and n is
the dimension of K. It is also announced that a local analogue of the Grothendieck
Conjecture still holds: all automorphisms of the absolute Galois group of K, which
are compatible with ramification filtration and satisfy some natural topological con­
ditions appear as conjugations via some automorphisms of the algebraic closure of
K.
0. Introduction
This paper deals with the formalism of ramification theory of higher dimensional
local fields. It comes from I.Zhukov's approach [Zh], [Ab5] to such a theory in the
case of 2­dimensional local fields K, which is based on the introduction of the
additional structure on K given by its closed 1­dimensional local subfield K c of
dimension 1 --- ``the subfield of 1­dimensional constants''. Then the filtration of
#K = Gal(K sep /K) by its ramification subgroups appears in the form of decreasing

  

Source: Abrashkin, Victor - Department of Mathematical Sciences, University of Durham

 

Collections: Mathematics