Seminar

The monochromatic layers of the chromatic filtration on spectra, that is- The K(n)-local (stable 00-)categories Sp_{K(n)} enjoy many remarkable properties. One example is the vanishing of the Tate construction due to  Hovey-Greenlees-Sadofsky.  The vanishing of Tate construction can be considered as a natural equivalence between the colimits and limits in Sp_{K(n)}  parametrized by finite groupoids. Hopkins and Lurie proved a generalization of this result where finite groupoids are replaced by arbitrary \pi-finite  00-groupoids. They named this phenomena "Ambidexitiry" or "higher semi-additivity". 

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I shall describe this phenomenon and will attempt to demonstrate that it creates a surprising amount of properties and structure that lies in the heart of chromatic homotopy.  In particular, higher semi-additivity can be used as a tool to study the somewhat less approachable version of "monochromatic layers", namely the T(n)-local categories. 

This is a joint work in progress with Shachar Carmeli and Lior Yanovski

Zoom link.

https://msri.zoom.us/s/585445592

Ambidexterity in Chromatic Homotopy