math.RT — Representation Theory
A note on counterexamples to homological conjectures
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.
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