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SUMMARY:Recovering a local field from its Galois group - Marius Leonhardt 
 (University of Cambridge)
DTSTART:20170207T143000Z
DTEND:20170207T153000Z
UID:TALK70813@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:What characteristics of a field can be deduced from its\nabsol
 ute Galois group? Does the Galois group uniquely determine the field?\nIt 
 turns out that the answer to this question depends on the "type" of field.
  For example\, any two finite fields have isomorphic absolute Galois group
 s\, whereas two number fields are isomorphic if and only if their Galois g
 roups are.\nIn the case of finite extensions of $\\Q_p$\, there are non-is
 omorphic fields with isomorphic Galois groups. However\, if one requires t
 he group isomorphism to respect the filtration given by the ramification s
 ubgroups\, then S. Mochizuki has shown that one can fully reconstruct the 
 field.\nIn this talk I will give an overview of the methods involved in Mo
 chizuki's proof\, focussing on the use of Hodge-Tate representations in th
 e construction of an isomorphism between two given fields. 
LOCATION:MR13
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