Abstract:
Tensor-triangulated geometry (tt-geometry) can be thought of as "higher Zariski geometry", where we attempt to employ analogies from classical algebraic geometry to certain triangulated categories or stable ∞-categories called tensor-triangulated categories (or tt-categories for short). We will study examples of tt-categories, understand the analogy of the prime-spectrum that shows up in this world, and encounter several classic theorems in a new light, such as the Neeman-Thomason theorem and Hopkins-Neeman theorem. We will also venture into modern tt-geometry, and visit topics such as affineness of so-called 2-schemes, and gluing of Balmer spectra.