Connections and Higgs bundles on curves defined over a number field

Fuente: arXiv
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Autori principali: Biswas, Indranil, Gurjar, Sudarshan
Natura: Preprint
Pubblicazione: 2025
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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