Greg Stevenson: Tensor triangular geometry - Lecture 1

Tensor triangular geometry asks us to think of symmetric monoidal triangulated categories like rings, and in return provides us with an analogue of affine algebraic geometry. With this analogy in mind I'll introduce the general theory: starting with an essentially small symmetric monoidal triangulated category we will construct its spectrum, which is a space parametrizing exact monoidal localizations, and discuss its properties, as well as looking at several examples.
We will then move on to some of the challenges in extending the theory to the compactly generated setting (i.e. allowing infinite coproducts) and issues with the analogy between tensor triangular and algebraic geometry. Provided time allows, our focus will be on the tensor triangulated analogue of fields, their utility in understanding localizations, and the diculty in constructing residue fields at points of the spectrum.

This video is part of a series of lectures during the HIM Summer School "Spectral methods in algebra, geometry, and topology"