Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908670526226432 |
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| author | Li, Ruoxi |
| author_facet | Li, Ruoxi |
| contents | We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let $X$ be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of semistable Higgs bundles on $X$. This recovers results of Fedorov, A. Soibelman and Y. Soibelman in characteristic zero, as well as those of Mozgovoy and Schiffmann for finite fields. We also obtain a simpler formula for the motivic classes of the stacks of Higgs bundles in the universal $λ$-ring quotient using Mellit's results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles Li, Ruoxi Algebraic Geometry We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let $X$ be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of semistable Higgs bundles on $X$. This recovers results of Fedorov, A. Soibelman and Y. Soibelman in characteristic zero, as well as those of Mozgovoy and Schiffmann for finite fields. We also obtain a simpler formula for the motivic classes of the stacks of Higgs bundles in the universal $λ$-ring quotient using Mellit's results. |
| title | Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.09861 |