Connections and Higgs bundles on curves defined over a number field
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912602430373888 |
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| author | Biswas, Indranil Gurjar, Sudarshan |
| author_facet | Biswas, Indranil Gurjar, Sudarshan |
| contents | Let $X_0$ be an irreducible smooth projective curve defined over $\overline{\mathbb Q}$ and $\mathbb E$ a vector bundle on $X_0$. We give a criterion for connections on the base change ${\mathbb E}\otimes_{\overline{\mathbb Q}}{\mathbb C} \rightarrow X_0\times_{{\rm Spec}\,\overline{\mathbb Q}} {\rm Spec}\,\mathbb{C} $ to $\mathbb C$ to be the base change of some connection on $\mathbb E$. A similar criterion is given for Higgs fields on ${\mathbb E}\otimes_{\overline{\mathbb Q}}{\mathbb C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connections and Higgs bundles on curves defined over a number field Biswas, Indranil Gurjar, Sudarshan Algebraic Geometry Number Theory Let $X_0$ be an irreducible smooth projective curve defined over $\overline{\mathbb Q}$ and $\mathbb E$ a vector bundle on $X_0$. We give a criterion for connections on the base change ${\mathbb E}\otimes_{\overline{\mathbb Q}}{\mathbb C} \rightarrow X_0\times_{{\rm Spec}\,\overline{\mathbb Q}} {\rm Spec}\,\mathbb{C} $ to $\mathbb C$ to be the base change of some connection on $\mathbb E$. A similar criterion is given for Higgs fields on ${\mathbb E}\otimes_{\overline{\mathbb Q}}{\mathbb C}$. |
| title | Connections and Higgs bundles on curves defined over a number field |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2509.19737 |