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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Higher arithmetic duality - John Rognes (Universit
 y of Oslo)
DTSTART;TZID=Europe/London:20250512T101500
DTEND;TZID=Europe/London:20250512T111500
UID:TALK230530AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/230530
DESCRIPTION:I will report on joint work in progress with Sanat
 h Devalapurkar andJeremy Hahn. &nbsp\;The singular
  cohomology of a closed\, oriented manifoldsatisfi
 es Poincar&eacute\; duality\, and the Galois cohom
 ology of a local numberfield satisfies Tate-Poitou
  duality. &nbsp\;We prove similar duality theorems
 for syntomic cohomology and topological cyclic hom
 ology of a class ofring spectra\, tentatively call
 ed higher local number rings\, subjectto an orient
 ability hypothesis. &nbsp\;This class of ring spec
 tra includestruncated Brown-Peterson spectra\, com
 plex and real topological K-theory\,topological mo
 dular forms\, and their unramified extensions. &nb
 sp\;The dualitytheorems come in reduced\, localize
 d and filtered versions\, analogous toknown refine
 ments of Tate-Poitou duality in the case of classi
 cal rings.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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