Given a compact Kähler manifold X, it is shown that pairs of the form $(E,\, D)$ , where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on E, produce a neutral Tannakian category. The corresponding pro-algebraic affine group scheme is studied. In particular, it is shown that this pro-algebraic affine group scheme for a compact Riemann surface determines uniquely the isomorphism class of the Riemann surface.

中文翻译：

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关于 Kähler 流形上可积连接的某些 Tannakian 范畴

给定一个紧致的 Kähler 流形X，它证明了 $(E,\, D)$ 形式的对，其中E是X上的平凡全纯向量丛，D是E上的可积全纯连接，产生中性 Tannakian类别。研究了相应的代数仿射群方案。特别是，它表明了这种紧黎曼曲面的前代数仿射群方案唯一地确定了黎曼曲面的同构类。