Some Observations About Motivic Tensor Triangulated Geometry over a Finite Field

  • Shane KellyEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 309)


We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of the tensor triangulated spectrum of the Morel–Voevodsky stable homotopy category over a finite field.


Tensor triangulated categories Motivic cohomology Finite fields Milnor-Witt K-theory 



I thank the organisers of the conference “Bousfield classes form a set: a workshop in memory of Tetsusuke Ohkawa” for the invitation to speak which led me to think about these things, and also for having organised such an interesting conference. I also thank Paul Balmer, Jens Hornbostel, and Denis-Charles Cisinski for interesting discussions about potential future work, Marc Hoyois for discussions about the étale homotopy type, and Jeremiah Heller and Kyle Ormsby for pointing out that an “elementary fact” I was using in the proof of Proposition 4.5 is actually a combination of theorems of Ayoub, Balmer, Gabber, and Riou.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyMeguro-kuJapan

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