On K-theory of complex algebraic curves, by Igor Nikolaev

We develop K-theory of a noncommutative C*-algebra O(k) connected to measured foliations. The Morita invariants of O(k) are shown to describe the structure sheaf O(X) of a projective scheme (X,O(X)), where X has complex dimension 1. A notion of "projective curvature" of complex algebraic curves is introduced. The main result is a generalization of Manin-Soibelman duality between elliptic curves and noncommutative tori to noncommutative surfaces of higher genus.

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