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arXiv · 0909.0062

Fundamental domains for congruence subgroups of SL2 in positive characteristic

Lisa Carbone·Leigh Cobbs·Scott H. Murray
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Abstract

In this work, we construct fundamental domains for congruence subgroups of $SL_2(F_q[t])$ and $PGL_2(F_q[t])$. Our method uses Gekeler's description of the fundamental domains on the Bruhat- Tits tree $X = X_{q+1}$ in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma.

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BibTeXRIS

Lisa Carbone, Leigh Cobbs, Scott H. Murray. 2009-09-01. Fundamental domains for congruence subgroups of SL2 in positive characteristic. https://arxiv.org/abs/0909.0062

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