Noncommutative localization

The Teichmüller functor maps the category of elliptic curves over the field of characteristic zero to a category of the Effros-Shen algebras [9]. In the present note, we extend the functor to include the elliptic curves over the field of characteristic p. In particular, it is shown that the localization of a commutative ring at the maximal ideal corresponds to a crossed product of the Effros-Shen algebra by the p-th power of its shift automorphism. The Cuntz-Krieger algebra is, therefore, an example of the noncommutative local ring.