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arXiv · 1810.10515

Betti numbers of Shimura curves and arithmetic three--orbifolds

Mikołaj Frączyk·Jean Raimbault
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Abstract

We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes relatively to hyperbolic volume.

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Mikołaj Frączyk, Jean Raimbault. 2018-10-24. Betti numbers of Shimura curves and arithmetic three--orbifolds. https://doi.org/10.2140/ant.2019.13.2359

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