3D mirror symmetry in positive characteristic
Abstract
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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