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Carlson's Associated-Prime Depth Conjecture

Algebra · posed by Jon F. Carlson, 1995 · disproved

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Statement

Is the depth of the mod-pp cohomology ring of every finite group realized as the dimension of one of its associated primes? For G=SmallGroup⁡(128,859)G = \operatorname{SmallGroup}(128, 859) over F‾2\overline{\mathbb{F}}_2 the ring has depth 22 while every associated-prime quotient has dimension at least 33.

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

  1. construction · #1

    TARS agent system, with Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu and Yuchen Yang

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    The candidate group was found by the TARS agent system (foundation model not disclosed); the counterexample is certified by exact GAP/Singular computations audited by the human authors.

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