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The period-index problem and Hodge theory

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arxiv 2212.12971 v1 pith:WVA4APZJ submitted 2022-12-25 math.AG

Aise Johan de Jong , Alexander Perry This is my paper · ORCID
classification math.AG
keywords brauerconjectureindexprovesmoothalgebraicallyapplicationarbitrary
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Conditional on the Lefschetz standard conjecture in degree 2, we prove that the index of a Brauer class on a smooth projective variety divides a fixed power of its period, uniformly in smooth families. In the other direction, we reinterpret in more classical terms recent work of Hotchkiss which gives Hodge-theoretic lower bounds on the index of Brauer classes. We also prove versions of our results over arbitrary algebraically closed base fields, and as an application construct qualitatively new counterexamples to the integral Tate conjecture.

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Cited by 2 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.

  2. 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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