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arXiv · 2008.11483

On certain Tannakian categories of integrable connections over Kaehler manifolds

Indranil Biswas·João Pedro dos Santos·Sorin Dumitrescu·Sebastian Heller
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Abstract

Given a compact Kaehler 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.

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Indranil Biswas, João Pedro dos Santos, Sorin Dumitrescu, Sebastian Heller. 2021-04-12. On certain Tannakian categories of integrable connections over Kaehler manifolds. https://arxiv.org/abs/2008.11483

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