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arXiv · 1707.09925

Quaternionic Arithmetic Lattices of Rank 2 and a Fake Quadric in Characteristic 2

Nithi Rungtanapirom
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Abstract

We construct a torsion-free arithmetic lattice in $\mathrm{PGL}_2(\mathbb{F}_2(\!(t)\!))\times\mathrm{PGL}_2(\mathbb{F}_2(\!(t)\!))$ arising from a quaternion algebra over $\mathbb{F}_2(z)$. It is the fundamental group of a square complex with universal covering $T_3\times T_3$, a product of trees with constant valency $3$, which has minimal Euler characteristic. Furthermore, our lattice gives rise to a fake quadric over $\mathbb{F}_2(\!(t)\!)$ by means of non-archimedean uniformization.

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BibTeXRIS

Nithi Rungtanapirom. 2019-04-16. Quaternionic Arithmetic Lattices of Rank 2 and a Fake Quadric in Characteristic 2. https://doi.org/10.1142/s0218196718500467

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