Aarhus Universitets segl

Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory

Andrew Baker (University of Glasgow)
Onsdag 6. november 2024 16:15–17:15 G3.1 (1532-314)
Mathematics seminar

The Joker is a famous, very singular example of an endotrivial module over the 8-dimension subHopf algebra of the mod 2 Steenrod algebra 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, the double and iterated double are also realisable, but then the process stops. In the chromatic world, the double versions give rise objects whose Morava K-theory at height 2 involve endotrivial modules over the quaternion group of order 8 which lives inside the corresponding Morava stabilizer group. This gives a somewhat surprising connection between endotriviality in two different contexts. I will explain this from both an algebraic and a stable homotopy perspective, and discuss some possible generalisations and broader aspects.

Organiseret af: AarHomAlg
Kontakt: Amit Shah Revideret: 18.09.2024