  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 is known as the Krichever
correspondence. It was applied in the theory of integrable systems,
particularly, for the KP and KdV equations. We show that the Krichever
construction can be generalized to the case of dimension 2. We also include a
known description of connection between the KP hierarchy in the Lax form and
the vector fields on infinite Grassmanian manifolds and a construction of the
semi-infinite monomes for the field k((z)) which is an important part of the
theory of Sato Grassmanian. The text was published in Communications in
Algebra, 29(2001), No.9, 4157-4181. This version includes a corrected proof of
the proposition 2. Also, we include some additional remarks on the deduction of
concrete equations from the Lax hierarchy and appendix 2.
