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

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

**Zoom link: https://princeton.zoom.us/j/96282936122**

**Passcode: 998749**

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 expand this last sentence, lay out some of the theory, give particular examples, and then dwell on applications to Spanier-Whitehead duality and to Picard groups.

This is joint work with Agnès Beaudry, Mike Hopkins, and Vesna Stojanoska.