Nori's fundamental group of nilpotent bundles is uniquely determined by H¹(X, O_X), H²(X, O_X) and the cup product on a geometrically connected smooth proper variety over a char-0 field.
For example, cohomology groups in degree≥3are totally missing from our discussion
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On iterated universal extensions and Nori's fundamental group of nilpotent bundles
Nori's fundamental group of nilpotent bundles is uniquely determined by H¹(X, O_X), H²(X, O_X) and the cup product on a geometrically connected smooth proper variety over a char-0 field.