Geodesic
On certain Tannakian categories of integrable connections over Kähler manifolds
Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1034-1061

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DOI

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.
DOI : 10.4153/S0008414X21000201
Mots-clés : Integrable holomorphic connection, Higgs bundle, neutral Tannakian category, complex torus, Torelli theorem 
Biswas, Indranil; Santos, João Pedro dos; Dumitrescu, Sorin; Heller, Sebastian. On certain Tannakian categories of integrable connections over Kähler manifolds. Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1034-1061. doi: 10.4153/S0008414X21000201
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     title = {On certain {Tannakian} categories of integrable connections over {K\"ahler} manifolds},
     journal = {Canadian journal of mathematics},
     pages = {1034--1061},
     year = {2022},
     volume = {74},
     number = {4},
     doi = {10.4153/S0008414X21000201},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000201/}
}
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