Algebra/Topology seminar

Speaker: Logan Hyslop

Title: Against the Nerves of Steel Conjecture

Abstract: Using a nilpotence theorem, Hopkins and Smith computed the thick subcategories of finite spectra, in other words they computed its so-called Balmer spectrum. Motivated by the connection between thick subcategory theorems and nilpotence theorems, Balmer defined the so-called “homological spectrum” of a tensor triangulated category which, in a certain precise sense, is the space one computes by proving a nilpotence theorem, and then conjectured that the natural comparison map it admits to the Balmer spectrum is a homeomorphism in general. In this talk, based on joint work with Tobias Barthel and Maxime Ramzi, we will discuss some free constructions in higher Zariski geometry, which provide counter-examples to this conjecture of Balmer.