On complex and noncommutative torus
نویسنده
چکیده
To every non-singular elliptic curve (complex torus) we assign a C∗algebra Tθ = {u, v | vu = e uv} known as noncommutative torus. It is shown that morphisms of elliptic curves generate Morita equivalence of the corresponding noncommutative tori. Real number θ we call projective curvature attached to the elliptic curve. It is proved that projective curvatures of isomorphic elliptic curves are modular equivalent numbers. We prove that projective curvature of elliptic curve with complex multiplication is a quadratic irrationality given by periodic continued fraction.
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