An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups
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Between tradition (Hilbert́s 12th Problem) and actual challenges (coding theory) we attack infinite two-dimensional Galois theory. From a number theoretic point of view we work over ℚ(x). Geometrically, one has to do with towers of Shimura surfaces and Shimura curves on them. We construct and investigate a tower of rational Picard modular surfaces with Galois groups isomorphic to the (double) octahedron group and of their (orbitally) uniformizing arithmetic groups acting on the complex 2-dimensional unit ball 𝔹.
KeywordsArithmetic groups congruence subgroups unit ball coverings Picard modular surfaces Baily-Borel compactification arithmetic curves modular curves
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