Manchester Geometry Seminar 2004/2005

In 1970's I. M. Krichever discovered a construction attaching to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. This construction was used in integrable systems theory. Now this construction is called the Krichever map. In the e-print math.AG/9911097 A. N. Parshin suggested a generalization of the Krichever map for the case of algebraic surfaces from the point of view of 2-dimensional local fields k((u))((t)).

We suggest a generalization of the Krichever map to the case of algebraic varieties of arbitrary dimension from the point of view of multidimensional local fields. In particular, we obtain new explicit acyclic resolutions of quasicoherent sheaves connected with multidimensional local fields. This talk is a development of the work math.AG/0003188.