BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tomer Schlank (Hebrew University)
DTSTART:20210222T213000Z
DTEND:20210222T223000Z
DTSTAMP:20260423T024538Z
UID:MITTop/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/24/">
 Cyclotomic Galois extensions in the chromatic homotopy</a>\nby Tomer Schla
 nk (Hebrew University) as part of MIT topology seminar\n\n\nAbstract\nThe 
 chromatic approach to stable homotopy theory is 'divide and conquer'. That
  is\, questions about spectra are studies through various localizations th
 at isolate pure height phenomena and then are put back together. For each 
 height n\, there are two main candidates for pure height localization. The
  first is the generally more accessible K(n)-localization and the second i
 s the closely related T(n)-localization. It is an open problem whether the
  two families of localizations coincide.\n\nOne of the main reasons that t
 he K(n)-local category is more amenable to computations is the existence o
 f well understood Galois extensions of the K(n)-local sphere.\n\nIn the ta
 lk\, I will present a generalization\, based on ambidexterity\, of the cla
 ssical theory of cyclotomic extensions\, suitable for producing non-trivia
 l Galois extensions in the T(n)-local and K(n)-local context. This constru
 ction gives a new family of Galois extensions of the T(n)-local sphere and
  allows to lift the well known maximal abelian extension of the K(n)-local
  sphere to the T(n)-local world.\n\nI will then describe some applications
 \, including the study of the T(n)-local Picard group\, a chromatic versio
 n of the Kummer theory\, and interaction with algebraic K-theory.\n\nThis 
 is a joint project with Shachar Carmeli and Lior Yanovski.\n
LOCATION:https://researchseminars.org/talk/MITTop/24/
END:VEVENT
END:VCALENDAR