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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the residue sequence in logarithmic THH - Tommy
  Lundemo (Bergische Universität Wuppertal)
DTSTART;TZID=Europe/London:20250603T153000
DTEND;TZID=Europe/London:20250603T163000
UID:TALK230590AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/230590
DESCRIPTION:While algebraic K-theory\, TC\, and THH all enjoy 
 a common localization property\, a key tool to stu
 dy the resulting cofiber sequences - d&eacute\;vis
 sage - is only available for algebraic K-theory. T
 here have been two major attempts to circumvent th
 is: The first\, due to Hesselholt--Madsen and Blum
 berg--Mandell\, involves a model of THH and TC of 
 Waldhausen categories that produces new localizati
 on sequences as an instance of Waldhausen's fibrat
 ion theorem. The second\, due to Rognes--Sagave--S
 chlichtkrull\, bypasses d&eacute\;vissage entirely
 . Instead\, they use Rognes' logarithmic THH to ge
 neralize a classical residue sequence involving lo
 garithmic differential forms to a cofiber sequence
  of cyclotomic spectra.\nI will report on work in 
 progress\, in which I will address the problem of 
 reconciling the localization property of THH with 
 that of its logarithmic counterpart. When combined
  with forthcoming work of Ramzi--Sosnilo--Winges\,
  this becomes closely related to the problem of re
 alizing logarithmic THH as the THH of a stable inf
 inity-category\, providing a candidate category of
  "logarithmic modules" in specific cases.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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