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arXiv · 2212.09074

On Borel's stable range of the twisted cohomology of $\mathrm{GL}(n,\mathbb{Z})$

Kazuo Habiro·Mai Katada
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Abstract

Borel's stability and vanishing theorem gives the stable cohomology of $\mathrm{GL}(n,\mathbb{Z})$ with coefficients in algebraic $\mathrm{GL}(n,\mathbb{Z})$-representations. We compute the improved stable range that Borel remarked about. In order to further improve Borel's stable range, we adapt the method of Kupers-Miller-Patzt to any algebraic $\mathrm{GL}(n,\mathbb{Z})$-representations.

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Kazuo Habiro, Mai Katada. 2022-12-18. On Borel's stable range of the twisted cohomology of $\mathrm{GL}(n,\mathbb{Z})$. https://arxiv.org/abs/2212.09074

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