Tensor-triangulated categories as generalised commutative rings

24/05/2019, 15:00 - 16:00 in MAP/0G/018

Balchin, Scott (Warwick)


Abstract:

Tensor-triangulated categories are categories which have enough structure that one can treat them as if they were commutative rings. For example, we have the notion of the prime spectrum of a tt-category, which is the analogue of the Zariski spectrum of a commutative ring. Being able to treat categories in this way gives us a lot of tools to study its local and global properties, as well as discuss phenomena such as localization and completion.

In this talk I aim to introduce the theory of tt-categories, with a focus on exploring common examples arising from stable homotopy theory, algebraic geometry, and modular representation theory.

Mathematical Sciences Research Centre