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SUMMARY:Higher arithmetic duality - John Rognes (University of Oslo)
DTSTART:20250512T091500Z
DTEND:20250512T101500Z
UID:TALK230530@talks.cam.ac.uk
DESCRIPTION:I will report on joint work in progress with Sanath Devalapurk
 ar andJeremy Hahn. &nbsp\;The singular cohomology of a closed\, oriented m
 anifoldsatisfies Poincar&eacute\; duality\, and the Galois cohomology of a
  local numberfield satisfies Tate-Poitou duality. &nbsp\;We prove similar 
 duality theoremsfor syntomic cohomology and topological cyclic homology of
  a class ofring spectra\, tentatively called higher local number rings\, s
 ubjectto an orientability hypothesis. &nbsp\;This class of ring spectra in
 cludestruncated Brown-Peterson spectra\, complex and real topological K-th
 eory\,topological modular forms\, and their unramified extensions. &nbsp\;
 The dualitytheorems come in reduced\, localized and filtered versions\, an
 alogous toknown refinements of Tate-Poitou duality in the case of classica
 l rings.
LOCATION:Seminar Room 1\, Newton Institute
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