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SUMMARY:Endotrivial modules for the quaternion group and iterated Jokers i
 n chromatic homotopy theory - Andrew Baker (University of Glasgow)
DTSTART:20240531T083000Z
DTEND:20240531T093000Z
UID:TALK217210@talks.cam.ac.uk
DESCRIPTION:The Joker is a famous\, very singular example of an endotrivia
 l module over the 8-dimension subHopf algebra of the mod 2 Steenrod algebr
 a generated by Sq^1 and Sq^2. It is known that this can be realised as the
  cohomology of two distinct Spanier-Whitehead dual spectra. Similarly\, th
 e double and iterated double are also realisable\, but then the process st
 ops. In the chromatic world\, the double versions give rise to objects who
 se Morava K-theory at height 2 involves endotrivial modules over the quate
 rnion group of order 8 which lives inside the corresponding Morava stabili
 zer group. This gives a somewhat surprising connection between endotrivial
 ity in two different contexts. I will explain how all this works and discu
 ss some possible generalisations to higher chromatic heights.
LOCATION:External
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