  In 70's there was discovered a construction how to attach to some
algebraic-geometric data an infinite-dimensional subspace in the space k((z))
of the Laurent power series. The construction was successfully used in the
theory of integrable systems, particularly, for the KP and KdV equations. There
were also found some applications to the moduli of algebraic curves. But there
remained a hard restriction by the case of curves, so by dimension 1. Recently,
it was pointed out by the author that there are some connections between the
theory of the KP-equations and the theory of n-dimensional local fields. From
this point of view it becomes clear that the Krichever construction should have
a generalization to the case of higher dimensions. This generalization is
suggested in the paper for the case of algebraic surfaces.
