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Dualizing spheres for compact p-adic analytic groups and duality in chromatic homotopy

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Agnès Beaudry and Paul Goerss
University of Colorado and Northwestern University
Mon, 2021-06-14 14:00 - 16:00
Parent event: 
MPIM Topology Seminar

Meeting ID: 916 5855 1117
Password: as before.
Contact: Aru Ray, Tobias Barthel,Viktoriya Ozornova
Slides are attached on the Talk's page or see our Nextcloud

In his celebrated and widely studied work on Galois cohomology, Serre wrote down a dualizing module for the category of modules over a compact p-adic analytic group. This controlled duality for group cohomology. These ideas can be vastly generalized, and in particular have expressions in stable homotopy theory. In the chromatic paradigm, stable homotopy theory can be divided into slices, one at each prime p and each integer n; these are the K(n)-local categories. The homotopy theory of these slices behave very much like that of the category of modules of a particular p-adic analytic group. Serre’s ideas can carry us a very long way and reveal a great deal of interesting structure. The point of this talk will be to explain and expand on these ideas. We will emphasize examples. 
This is joint work with Mike Hopkins, and Vesna Stojanoska.

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