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SUMMARY:Ambidexterity in the T(n)-Local Stable Homotopy Theory - Lior Yano
 vski (Max-Planck-Institut für Mathematik\, Bonn)
DTSTART:20180828T143000Z
DTEND:20180828T153000Z
UID:TALK109120@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The monochromatic layers of the chromatic filtration on spectr
 a\, that is The K(n)-local (stable 00-)categories Sp_{K(n)} enjoy many rem
 arkable properties. One example is the vanishing of the Tate construction 
 due to&nbsp\; Hovey-Greenlees-Sadofsky.&nbsp\; The vanishing of Tate const
 ruction can be considered as a natural equivalence between the colimits an
 d limits in Sp_{K(n)}&nbsp\; parametrized by finite groupoids. Hopkins and
  Lurie proved a generalization of this result where finite groupoids are r
 eplaced by arbitrary \\pi-finite&nbsp\; 00-groupoids. There is another pos
 sible sequence of&nbsp\; (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 Kuh
 n. We shall prove that the analog of&nbsp\; Hopkins and Lurie&#39\;s resul
 t in for Sp_{T(n)}.&nbsp\; Our proof will also give an alternative proof f
 or the K(n)-local case. This is a joint work with Shachar Carmieli and Lio
 r Yanovski
LOCATION:Seminar Room 2\, Newton Institute
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