In joint work with Greg Stevenson, we prove that the frame of smashing tensor ideals of a big tt-category is always spatial. As such, by Stone duality, we are afforded a space: the smashing spectrum. In this talk, I will report on the construction of this new invariant via lattice theoretic techniques, and its relation to the Balmer spectrum. In particular, we will see that there is a surjective comparison map which detects the failure of the telescope conjecture.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
