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Carlson's Associated-Prime Depth Conjecture

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carlson-depth-conjectureAlgebraposed by Jon F. Carlson, 1995recorded: disproved

1 attempt · no person has looked

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.

Context

Carlson's 1995 conjecture in modular representation theory.

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1 attempt

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  • #1

    Attempt 1

    constructionTARS agent system with Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu, Yuchen Yang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    TARS agent system
    people
    Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu, Yuchen Yang

    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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