On complex and noncommutative tori

Details On complex and noncommutative tori On complex and noncommutative tori

2002-12-23

arxiv.org/abs/math/0212324v2

Proc. Amer. Math. Soc. 134 (2006), 973-981

Mathematics

Algebraic Geometry

13 pages, straighten version, to appear Proc. Amer. Math. Soc

Scientific paper

10.1090/S0002-9939-05-08244-4

The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main result says that under the morphism isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.

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