{"id":"hexagon/2610.00143","pdf":"https://hexagonmath.org/pdf/2610.00143v5","url":"https://hexagonmath.org/abs/2610.00143v5","tags":["math.RA","msc:16D50","msc:16E10","Representation theory"],"score":0,"title":"A note on counterexamples to homological conjectures","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.RT","summary":"Building on the constructions of OpenAI, we extend these constructions to any base field containing an element of infinite multiplicative order. Over each such field, we obtain finite-dimensional algebras giving counterexamples to both Tachikawa conjectures, the Auslander–Reiten conjecture, the Gorenstein-projective conjecture, the Nakayama, generalized Nakayama, and strong Nakayama conjectures, the Auslander–Gorenstein conjecture, the little and big finitistic dimension conjectures, and the Wakamatsu tilting conjecture. 2026.10.15:Version 3 of this manuscript has completed a full-paper…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"none"}