Krichever correspondence for algebraic varieties

Details Krichever correspondence for algebraic varieties Krichever correspondence for algebraic varieties

2000-03-28

arxiv.org/abs/math/0003188v1

Izv. Math. 65 (2001), no. 5, 941-975

Mathematics

Algebraic Geometry

38 pages, LaTex, to appear in "Izvestiya RAN"

Scientific paper

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. Now this construction is called the Krichever map. In 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. In this work 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. For surfaces our construction coincides with the Parshin construction. Besides, we obtain new explicit acyclic resolutions of quasicoherent sheaves connected with multidimensional local fields.

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