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Dualizing spheres for p-adic Lie groups, with applications to chromatic homotopy theory

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 25, 2019 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Vesna Stojanoska (University of Illinois at Urbana-Champaign)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • equivariant duality

  • p-adic Lie group

  • spherical bundle

  • Lubin-Tate

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

I will describe a Linearization Conjecture that identifies the spectral dualizing module of a p-adic Lie group in terms of a representation sphere built from the Lie algebra. We can prove this when the action is restricted to certain small finite subgroups. These results are enough to determine Spanier-Whitehead duals of some chromatically interesting spectra. This is joint work in progress with Beaudry, Goerss, and Hopkins.

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