Intersection pairing for arithmetic cycles with degenerate Green currents

1998/03/13 by Atsushi Moriwaki, Moriwaki, Atsushi
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9803054

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openalex publication_date 1998/03/13 · arxiv created 1998/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we would like to propose a suitable extension of the arithmetic Chow group of codimension one, in which the Hodge index theorem holds. We also prove an arithmetic analogue of Bogomolov's instability theorem for rank 2 vector bundles on arbitrary regular projective arithmetic varieties.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Related

• Higher Arithmetic Intersection Theory
• Hodge index theorem for arithmetic cycles of codimension one
• Arithmetic Intersection Theory on Deligne-Mumford Stacks
• The arithmetic Hodge index theorem for adelic line bundles I
• A local version of the arithmetic Hodge index theorem over quasiprojective varieties