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- W2963507907 abstract "Given an imaginary quadratic extension $K$ of $mathbb{Q}$, we give a classification of the maximal nonelementary subgroups of the Picard modular group $operatorname{PSU}_{1,2}(mathcal{O}_K)$ preserving a complex geodesic in the complex hyperbolic plane $mathbb{H}^2_mathbb{C}$. Complementing work of Holzapfel, Chinburg-Stover and Moller-Toledo, we show that these maximal $mathbb{C}$-Fuchsian subgroups are arithmetic, arising from a quaternion algebra $Big(!begin{array}{c} D,,D_Khlinemathbb{Q}end{array} !Big)$ for some explicit $Dinmathbb{N}-{0}$ and $D_K$ the discriminant of $K$. We thus prove the existence of infinitely many orbits of $K$-arithmetic chains in the hypersphere of $mathbb{P}_2(mathbb{C})$." @default.
- W2963507907 created "2019-07-30" @default.
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- W2963507907 date "2017-09-22" @default.
- W2963507907 modified "2023-09-24" @default.
- W2963507907 title "A classification of $mathbb{C}$-Fuchsian subgroups of Picard modular groups" @default.
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- W2963507907 doi "https://doi.org/10.7146/math.scand.a-26128" @default.
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