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On certain Tannakian categories of integrable connections over Kähler manifolds
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 74 / Issue 4 / August 2022
- Published online by Cambridge University Press:
- 21 April 2021, pp. 1034-1061
- Print publication:
- August 2022
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- Article
- Export citation
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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.
