Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916668084584448 |
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| author | Herrero, Andres Fernandez Zhang, Siqing |
| author_facet | Herrero, Andres Fernandez Zhang, Siqing |
| contents | Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of $G$-bundles on the fibers of $C$ equipped with $t$-connections with pole orders bounded by $D$. Under mild assumptions on the characteristics of all the residue fields of $S$, we construct a Hodge moduli space $M_{Hod, G} \to \mathbb{A}^1_S$ for the semistable locus, construct a Harder-Narasimhan stratification, and thus obtain a semistable reduction theorem. If all the fibers of the divisor of poles $D$ are nonempty, then we show that the stack of semistable objects is smooth over $\mathbb{A}^1_{S}$. We also define a Hodge-Hitchin morphism in positive characteristic and prove that it is proper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16755 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic Herrero, Andres Fernandez Zhang, Siqing Algebraic Geometry Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of $G$-bundles on the fibers of $C$ equipped with $t$-connections with pole orders bounded by $D$. Under mild assumptions on the characteristics of all the residue fields of $S$, we construct a Hodge moduli space $M_{Hod, G} \to \mathbb{A}^1_S$ for the semistable locus, construct a Harder-Narasimhan stratification, and thus obtain a semistable reduction theorem. If all the fibers of the divisor of poles $D$ are nonempty, then we show that the stack of semistable objects is smooth over $\mathbb{A}^1_{S}$. We also define a Hodge-Hitchin morphism in positive characteristic and prove that it is proper. |
| title | Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2307.16755 |