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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19695 |
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| _version_ | 1866909552001155072 |
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| author | Bao, Vo Quoc Hai, Phung Ho Van Thinh, Dao |
| author_facet | Bao, Vo Quoc Hai, Phung Ho Van Thinh, Dao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of the differential fundamental group of algebraic curves Bao, Vo Quoc Hai, Phung Ho Van Thinh, Dao Algebraic Geometry 14F40, 14F43, 14L15, 18G15, 18G40, 18M25 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. |
| title | Cohomology of the differential fundamental group of algebraic curves |
| topic | Algebraic Geometry 14F40, 14F43, 14L15, 18G15, 18G40, 18M25 |
| url | https://arxiv.org/abs/2503.19695 |