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arXiv · 2312.02100

Quantum Steenrod operations of symplectic resolutions

Jae Hee Lee
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Abstract

We study the mod $p$ equivariant quantum cohomology of conical symplectic resolutions. Using symplectic genus zero enumerative geometry, Fukaya and Wilkins defined operations on mod $p$ quantum cohomology deforming the classical Steenrod operations on mod $p$ cohomology. We conjecture that these quantum Steenrod operations on divisor classes agree with the $p$-curvature of the mod $p$ equivariant quantum connection, and verify this in the case of the Springer resolution. The key ingredient is a new compatibility relation between the quantum Steenrod operations and the shift operators.

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Jae Hee Lee. 2023-12-04. Quantum Steenrod operations of symplectic resolutions. https://doi.org/10.2140/gt.2025.29.4341

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