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SUMMARY:Representations of Galois groups and Algebraic K-theory of fields 
 - Gunnar Carlsson (Stanford University)
DTSTART:20220613T090000Z
DTEND:20220613T100000Z
UID:TALK174890@talks.cam.ac.uk
DESCRIPTION:We have shown in earlier work that there is a strong relations
 hip between derived completions of representation rings of absolute Galois
  groups and Milnor K-theory\, and that this relationship derives from a sp
 ectrum level construction relating a completion of the K-theory spectrum o
 f the category of finite dimensional representations of the absolute Galoi
 s group of a field F with &nbsp\;the K-theory spectrum of F. We will descr
 ibe this relationship and progress toward a proof of the main conjecture\,
  namely that the the completion of the representation theory spectrum is e
 quivalent to the K-theory spectrum of the field. &nbsp\;This is joint work
  with Roy Joshua.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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