Motivic invariants of moduli stacks of Higgs bundles and bundles with connections: results and speculations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917257286778880 |
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| author | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| author_facet | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| contents | We review some results and techniques from our papers devoted to the computation of motivic classes of stacks of parabolic Higgs budles and bundles with connections on a curve. In the last section we present some directions for future work, as well as some speculations. The latter include a generalization of the P=W conjecture inspired by the work of Maxim Kontsevich and the third author on the Riemann--Hilbert correspondence for complex symplectic manifolds as well as our running project on the motivic classes of the moduli stacks of nilpotent pairs on the formal disk and geometric Satake correspondence for double affine Grassmannians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07713 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Motivic invariants of moduli stacks of Higgs bundles and bundles with connections: results and speculations Fedorov, Roman Soibelman, Alexander Soibelman, Yan Algebraic Geometry High Energy Physics - Theory Quantum Algebra Symplectic Geometry 14J60 We review some results and techniques from our papers devoted to the computation of motivic classes of stacks of parabolic Higgs budles and bundles with connections on a curve. In the last section we present some directions for future work, as well as some speculations. The latter include a generalization of the P=W conjecture inspired by the work of Maxim Kontsevich and the third author on the Riemann--Hilbert correspondence for complex symplectic manifolds as well as our running project on the motivic classes of the moduli stacks of nilpotent pairs on the formal disk and geometric Satake correspondence for double affine Grassmannians. |
| title | Motivic invariants of moduli stacks of Higgs bundles and bundles with connections: results and speculations |
| topic | Algebraic Geometry High Energy Physics - Theory Quantum Algebra Symplectic Geometry 14J60 |
| url | https://arxiv.org/abs/2602.07713 |