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arXiv · 2401.14205

On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one

Werner Mueller·Frédéric Rochon
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Abstract

Given a number field $F$ with ring of integers $\mathcal{O}_{F}$, one can associate to any torsion free subgroup of $\operatorname{SL}(2,\mathcal{O}_{F})$ of finite index a complete Riemannian manifold of finite volume with fibered cusp ends. For natural choices of flat vector bundles on such a manifold, we show that analytic torsion is identified with the Reidemeister torsion of the Borel-Serre compactification. This is used to obtain exponential growth of torsion in the cohomology for sequences of congruence subgroups.

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Werner Mueller, Frédéric Rochon. 2024-01-25. On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one. https://arxiv.org/abs/2401.14205

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