Presented by:
Lior Yanovski
Date:
Tuesday 28th August 2018 - 15:30 to 16:30
Venue:
INI Seminar Room 2
Abstract:
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. There is another possible sequence of (stable 00-)categories who can be considered
as "monochromatic layers", Those are the T(n)-local 00-categories
Sp_{T(n)}. For the Sp_{T(n)} the vanishing of the Tate
construction was proved by Kuhn. We shall prove that the analog of Hopkins and Lurie's result in for Sp_{T(n)}. Our proof will also give an alternative proof for
the K(n)-local case. This is a joint work with Shachar Carmieli and Lior
Yanovski
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