Tensor triangular geometry -- Notes for an Oberwolfach Seminar

TL;DR

This paper develops support notions for triangulated categories and applies them to classify tensor ideals in categories from modular representation theory, based on lecture notes from an Oberwolfach seminar.

Contribution

It introduces new support concepts for triangulated categories and uses them to classify tensor ideals in modular representation theory contexts.

Findings

Classified thick tensor ideals in modular representation categories.

Developed new support theories for triangulated categories.

Provided foundational notes for tensor triangular geometry.

Abstract

These are the notes from lectures I gave at the Oberwolfach Seminar "Tensor Triangular Geometry and Interactions" which was held in October 2025. The aim of these notes is twofold: We develop notions of support for triangulated categories, and we apply them to classify thick and localising tensor ideals of categories that arise in modular representation theory of finite groups.