Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 199-02. A counterexample to Tachikawa's second conjecture
Manuscript map · lines 5965–5974
OpenAI@2026-10-07#rem:oai-p-199-02
Authors: OpenAI. Family 199.
Title: A counterexample to Tachikawa's second conjecture.
Abstract: We disprove Tachikawa's second conjecture by constructing a finite-dimensional symmetric algebra over $k={}mathbb F_2(q,H_1,H_2)$ with a finite-dimensional nonprojective module whose self-extension groups vanish in every positive degree. The associated endomorphism algebra also gives counterexamples to the classical, generalized, and strong Nakayama conjectures, the Auslander–Gorenstein conjecture, and the Wakamatsu tilting conjecture. These conclusions persist after every extension of k.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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