Geometric Theory of Parshin's Residues. Toric Neighborhoods of Parshin's Points

Mathematics – Algebraic Geometry

Scientific paper

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24 pages; no pictures;

Scientific paper

The paper consist of two parts. In the first part we introduce flags of lattices and associated injective systems of (non-normal) cones and projective systems of (non-normal) affine toric varieties. We study the associated field of multidimensional Laurent power series. In the second part we use the resolution of singularities techniques to study the geometry near a complete flag of subvarieties and the Parshin's residues. The first part plays the role of a standard coordinate neighborhood for Parshin's points.

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