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Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields

Algebra · posed by Auslander, Reiten and Smalø · solved

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Statement

For a perfect field kk and a representation-infinite finite-dimensional kk-algebra AA, the Auslander–Reiten quiver of AA has infinitely many connected components. This establishes a conjecture of Auslander, Reiten and Smalø, for finite-dimensional algebras over perfect fields.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Wen Chang and Quanyu Tang, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The authors credit ChatGPT with the technical construction and verification of the semilinear twist argument in Lemma 4, and say it was used more substantially in extending the result from algebraically closed fields to arbitrary perfect fields - the step that gives the paper its stated generality.

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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