### 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.

Igor Nikolaev <inikolae@fields.utoronto.ca>