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Uniform stability of ranks

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arxiv 2411.03412 v1 pith:YZOJUDAI submitted 2024-11-05 math.CO

Guy Moshkovitz , Daniel G. Zhu This is my paper · ORCID
classification math.CO
keywords fieldanalysisanalyticassumingassumptionbasecarefulchen
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Chen and Ye recently proved that the analytic rank of tensors is stable under field extensions, assuming a fixed base field. Using a more careful analysis, we show that this assumption is unnecessary.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lower bounds on the strength of the determinant

    math.AC 2026-07 accept novelty 8.0 of 10

    The determinant has strength p for prime p and partition rank n minus o(n), proved by a new Chern class obstruction.

  2. Slice rank and partition rank of the determinant

    math.CO 2025-09 conditional novelty 8.0 of 10

    The determinant has slice rank n, partition rank at least log2(n)+1, and the 4x4 determinant has partition rank 3, giving the first unbounded separation between partition rank and analytic rank.

  3. Bounds for Geometric rank in Terms of Subrank

    math.CO 2025-06 conditional novelty 8.0 of 10

    For tensors of any fixed order, geometric rank is bounded by a function of subrank, and for order-three tensors the bound is quadratic, over every field.

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