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arXiv · 2402.10068

Cohomology groups with compact support for flat line bundles on certain complex Lie groups

Takayuki Koike·Jinichiro Tanaka
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Abstract

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.

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Takayuki Koike, Jinichiro Tanaka. 2024-02-15. Cohomology groups with compact support for flat line bundles on certain complex Lie groups. https://arxiv.org/abs/2402.10068

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