Quantum Adams operations in quasimap K-theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915544624529408 |
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| author | Bai, Shaoyun Lee, Jae Hee |
| author_facet | Bai, Shaoyun Lee, Jae Hee |
| contents | We define quantum deformations of Adams operations in $K$-theory, in the framework of quasimap quantum $K$-theory. They provide $K$-theoretic analogs of the quantum Steenrod operations from equivariant symplectic Gromov--Witten theory. We verify the compatibility of these operations with the Kahler and equivariant $q$-difference module structures, provide sample computations via $\mathbb{Z}/k$-equivariant localization, and identify them with $p$-curvature operators of the Kahler $q$-difference connections as studied in Koroteev-Smirnov. We also formulate and verify a $K$-theoretic quantum Hikita conjecture at roots of unity, and propose an indirect algebro-geometric definition of quantum Steenrod operations |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Adams operations in quasimap K-theory Bai, Shaoyun Lee, Jae Hee Algebraic Geometry Representation Theory Symplectic Geometry We define quantum deformations of Adams operations in $K$-theory, in the framework of quasimap quantum $K$-theory. They provide $K$-theoretic analogs of the quantum Steenrod operations from equivariant symplectic Gromov--Witten theory. We verify the compatibility of these operations with the Kahler and equivariant $q$-difference module structures, provide sample computations via $\mathbb{Z}/k$-equivariant localization, and identify them with $p$-curvature operators of the Kahler $q$-difference connections as studied in Koroteev-Smirnov. We also formulate and verify a $K$-theoretic quantum Hikita conjecture at roots of unity, and propose an indirect algebro-geometric definition of quantum Steenrod operations |
| title | Quantum Adams operations in quasimap K-theory |
| topic | Algebraic Geometry Representation Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2510.09335 |