Canonical Models of Arithmetic
نویسندگان
چکیده
In 1983 Takeuchi showed that up to conjugation there are exactly 4 arithmetic subgroups of PSL2(R) with signature (1;∞). Shinichi Mochizuki gave a purely geometric characterization of the corresponding arithmetic (1;∞)-curves, which also arise naturally in the context of his recent work on inter-universal Teichmüller theory. Using Bely̆ı maps, we explicitly determine the canonical models of these curves. We also study their arithmetic properties and modular interpretations.
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