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arXiv · 2503.19695

Cohomology of the differential fundamental group of algebraic curves

Vo Quoc Bao·Phung Ho Hai·Dao Van Thinh
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Abstract

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates the relationship between the de Rham cohomology of a vector bundle with connection and the group cohomology of the corresponding representation of the differential fundamental group of X . Consequently, we obtain some vanishing and non-vanishing results for the group cohomology.

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Vo Quoc Bao, Phung Ho Hai, Dao Van Thinh. 2025-03-25. Cohomology of the differential fundamental group of algebraic curves. https://arxiv.org/abs/2503.19695

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