An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups
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چکیده
Between tradition (Hilbert’s 12-th 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 along a Galois group isomorphic to the (double) octahedron group and of their (orbitally) uniformizing arithmetic groups acting on the complex 2-dimensional unit ball B.
منابع مشابه
Invariants of some compactified Picard modular surfaces and applications
The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are also discussed.
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