Duality for arithmetic Dijkgraaf-Witten theory
Number Theory
2025-08-27 v1
Abstract
Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X subset spec O_F. For the full ring of integers X = spec O_F, we give examples with quadratic fields and the quaternion group Q_8 where these equivalences fail, but also identify sufficient conditions under which they still hold.
Keywords
Cite
@article{arxiv.2508.19214,
title = {Duality for arithmetic Dijkgraaf-Witten theory},
author = {Jaro Eichler},
journal= {arXiv preprint arXiv:2508.19214},
year = {2025}
}