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3D mirror symmetry in positive characteristic

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arxiv 2503.23590 v2 pith:WNKS3GR3 submitted 2025-03-30 math.RT math.SG

3D mirror symmetry in positive characteristic

Shaoyun Bai , Jae Hee Lee This is my paper
classification math.RT math.SG
keywords mirrorcharacteristichikitaquantumsymmetryactionarithmeticaspect
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Via the formulation of (quantum) Hikita conjecture with coefficients in a characteristic $p$ field, we explain an arithmetic aspect of the theory of 3D mirror symmetry. Namely, we propose that the action of Steenrod-type operations and Frobenius-constant quantizations intertwine under the (quantum) Hikita isomorphism for 3D mirror pairs, and verify this for the Springer resolutions and hypertoric varieties.

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Cited by 2 Pith papers

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

  1. The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology

    math.QA 2026-01 conditional novelty 8.0

    Over a field of characteristic p, all Kontsevich-Soibelman operations on periodic cyclic homology are generated by the p-fold equivariant cap product and commute with the Getzler-Gauss-Manin connection.

  2. Quantum Steenrod powers and Hamiltonian maps

    math.SG 2026-07 conditional novelty 7.0

    Hamiltonian pseudo-rotations and finite-order Hamiltonian diffeomorphisms force geometric uniruledness; new criteria (non-torsion orbits, symplectically degenerate maxima, reversed Hofer–Zehnder) force infinitely many...