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The period-index conjecture for abelian threefolds and Donaldson-Thomas theory

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arxiv 2405.03315 v2 pith:56YTH5BG submitted 2024-05-06 math.AG

James Hotchkiss , Alexander Perry This is my paper · ORCID
classification math.AG
keywords abelianconjecturehodgeperiod-indexthreefoldsclassesdonaldson-thomasintegral
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We prove the period-index conjecture for unramified Brauer classes on abelian threefolds. To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional Calabi-Yau categories, with the feature that the noncommutative variational integral Hodge conjecture holds for classes with nonvanishing invariant. The period-index result is then proved by interpreting it as the algebraicity of a Hodge class on the twisted derived category, and specializing within the Hodge locus to an untwisted abelian threefold with nonvanishing invariant. As a consequence, we also deduce the integral Hodge conjecture for generically twisted abelian threefolds.

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Cited by 7 Pith papers

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

  1. The period-index conjecture is false

    math.AG 2026-08 accept novelty 8.0 of 10

    The period-index conjecture is disproved: for every d≥3 there is a variety with a 2-torsion Brauer class of index 2^{d-1}, exceeding the conjectural bound.

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  7. The period-index problem for hyper-K\"ahler varieties via hyperholomorphic bundles

    math.AG 2025-02 accept novelty 6.0 of 10

    For K3^{[n]}-type hyper-Kähler varieties, the index of a Brauer class divides a power of its period, with exponent equal to the dimension in general and half the dimension for most classes in Picard rank at least two.

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