Quantum Steenrod operations of symplectic resolutions

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.

35 pages, comments welcome! v2: added references, fixed minor typos; v3: accepted version

References in corpus (6)

• Floer theory for negative line bundles via Gromov-Witten invariants
• A construction of the quantum Steenrod squares and their algebraic relations
• Shift operators and toric mirror theorem
• Covariant constancy of quantum Steenrod operations
• Formal groups and quantum cohomology
• Flat endomorphisms for mod $p$ equivariant quantum connections from quantum Steenrod operations