Higher arithmetic duality

Add to your list(s) Download to your calendar using vCal

• John Rognes (University of Oslo)
• Monday 12 May 2025, 10:15-11:15
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

EHTW03 - New horizons for equivariance in homotopy theory

I will report on joint work in progress with Sanath Devalapurkar andJeremy Hahn.  The singular cohomology of a closed, oriented manifoldsatisfies Poincaré duality, and the Galois cohomology of a local numberfield satisfies Tate-Poitou duality.  We prove similar duality theoremsfor syntomic cohomology and topological cyclic homology of a class ofring spectra, tentatively called higher local number rings, subjectto an orientability hypothesis.  This class of ring spectra includestruncated Brown-Peterson spectra, complex and real topological K-theory,topological modular forms, and their unramified extensions.  The dualitytheorems come in reduced, localized and filtered versions, analogous toknown refinements of Tate-Poitou duality in the case of classical rings.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.