Cohomology groups with compact support for flat line bundles on certain complex Lie groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912164460101632 |
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| author | Koike, Takayuki Tanaka, Jinichiro |
| author_facet | Koike, Takayuki Tanaka, Jinichiro |
| contents | Let $X$ be a complex surface obtained as the quotient of the complex Euclidean space $\mathbb{C}^2$ by a discrete subgroup of rank $3$. We investigate the cohomology group $H_0^1(X, E)$ with compact support for a unitary flat line bundle $E$ over $X$. We show the vanishing of $H_0^1(X, E)$ for a certain class of such pairs $(X, E)$, which includes infinitely many examples such that $H^1(X, E)$ is non-Hausdorff and infinite dimensional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology groups with compact support for flat line bundles on certain complex Lie groups Koike, Takayuki Tanaka, Jinichiro Complex Variables 32F32, 53C55 Let $X$ be a complex surface obtained as the quotient of the complex Euclidean space $\mathbb{C}^2$ by a discrete subgroup of rank $3$. We investigate the cohomology group $H_0^1(X, E)$ with compact support for a unitary flat line bundle $E$ over $X$. We show the vanishing of $H_0^1(X, E)$ for a certain class of such pairs $(X, E)$, which includes infinitely many examples such that $H^1(X, E)$ is non-Hausdorff and infinite dimensional. |
| title | Cohomology groups with compact support for flat line bundles on certain complex Lie groups |
| topic | Complex Variables 32F32, 53C55 |
| url | https://arxiv.org/abs/2402.10068 |