数域上曲线上的连接和希格斯束

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-29 DOI:10.1016/j.geomphys.2025.105664

Indranil Biswas , Sudarshan Gurjar

引用次数: 0

摘要

设X0是一条定义在Q面上的不可约光滑投影曲线，E是X0上的向量束。我们给出了一个关于E⊗Q - C - X0×SpecQ的连接的基变化的准则E⊗Q - C上的连接是E上的一些连接的基变化的准则。对于E⊗Q - C上的希格斯场也给出了类似的准则

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Connections and Higgs bundles on curves defined over a number field

Let

X_{0}

be an irreducible smooth projective curve defined over

\overline{Q}

and

E

a vector bundle on

X_{0}

. We give a criterion for connections on the base change

E \otimes_{\overline{Q}} C ⟶ X_{0} \times_{Spec \overline{Q}} Spec C

C

to be the base change of some connection on

E

. A similar criterion is given for Higgs fields on

E \otimes_{\overline{Q}} C

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity