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SUMMARY:Galois characteristics of local fields - Marius Leonhardt\, Univer
 sity of Cambridge
DTSTART:20161111T150000Z
DTEND:20161111T160000Z
UID:TALK68830@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:What characteristics of a field can be deduced from its\nabsol
 ute Galois group? Does the Galois group uniquely determine the field? It t
 urns out that the answer to this question depends on the "type" of\nfield.
  For example\, any two finite fields have isomorphic absolute\nGalois grou
 ps\, whereas two number fields are isomorphic if and only if\ntheir Galois
  groups are. In the case of finite extensions of $\\Q_p$\, there are non-i
 somorphic\nfields with isomorphic Galois groups. However\, if one requires
  the group\nisomorphism to respect the filtration given by the ramificatio
 n\nsubgroups\, then S. Mochizuki has showed that one can fully reconstruct
 \nthe field. In this talk I will give an overview of the methods involved 
 in\nMochizuki's proof\, focussing on local class field theory on the one h
 and\nand Hodge-Tate representations on the other.
LOCATION:CMS\, MR15
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