On geometrically reductive tensor categories
Representation Theory
2026-05-20 v1
Abstract
We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also reduce two further conjectures concerning geometric reductivity for tensor categories to other conjectures appearing in the literature.
Cite
@article{arxiv.2605.19167,
title = {On geometrically reductive tensor categories},
author = {Kevin Coulembier},
journal= {arXiv preprint arXiv:2605.19167},
year = {2026}
}