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SUMMARY:A local analog of the Grothendieck conjecture for higher local fie
 lds - Abrashkin\, V (Durham)
DTSTART:20090825T083000Z
DTEND:20090825T093000Z
UID:TALK19585@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Suppose K is an N-dimensional local field where N is a non-neg
 ative integer. By definition\, if N=0 then K is just a finite field\, othe
 rwise\, K is a complete discrete valuation field and its residue field is 
 an (N-1)-dimensional local field. Let G be the absolute Galois group of K.
  If N=1 then the structure of the topological group G depends only on very
  weak invariants of K and is not sufficient to recover uniquely the field 
 K. The situation becomes totally different if we take into account the fil
 tration of G by its ramification subgroups. Then the corresponding functor
  from the category of 1-dimensional local fields to the category of profin
 ite groups with decreasing filtration is fully faithful. In the talk it wi
 ll be discussed an analog of this statement for higher local fields and it
 s relation to the Grothendieck conjecture in the context of global fields.
  
LOCATION:Seminar Room 1\, Newton Institute
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