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{\Large Department of Mathematics, BGU}

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{\Huge AGNT}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, January  2, 2019}
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\textbf{At} \emph{15:10 -- 16:25}
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\textbf{In} \emph{-101}

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{\large\scshape Tomer Schlank 
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  (HUJI)
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will talk about
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{\Large\bfseries Ambidexterity in the T(n)-Local Stable Homotopy Theory\par}
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\textsc{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 the 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 \textbackslash{}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 Carmeli and Lior Yanovski








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