Krichever correspondence for algebraic varieties

Abstract

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.

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

References in corpus (3)

• On a Ring of Formal Pseudo-differential Operators
• On a relative version of the Krichever correspondence
• Krichever Correspondence for Algebraic Surfaces

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• Local analog of the Deligne-Riemann-Roch isomorphism for line bundles in relative dimension $1$
• On adelic quotient group for algebraic surface
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• A Relative Lubin-Tate Theorem via Meromorphic Formal Geometry
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