The arithmetic Hodge index theorem for adelic line bundles

Xinyi Yuan; Shou Wu Zhang

doi:10.1007/s00208-016-1414-1

The arithmetic Hodge index theorem for adelic line bundles

Xinyi Yuan
, Shou Wu Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

In this paper, we prove index theorems for integrable metrized line bundles on projective varieties over complete fields and number fields respectively. As applications, we prove a non-archimedean analogue of the Calabi theorem and a rigidity theorem about the preperiodic points of algebraic dynamical systems.

Original language	English (US)
Pages (from-to)	1123-1171
Number of pages	49
Journal	Mathematische Annalen
Volume	367
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-016-1414-1
State	Published - Apr 1 2017

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-016-1414-1

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title = "The arithmetic Hodge index theorem for adelic line bundles",

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AB - In this paper, we prove index theorems for integrable metrized line bundles on projective varieties over complete fields and number fields respectively. As applications, we prove a non-archimedean analogue of the Calabi theorem and a rigidity theorem about the preperiodic points of algebraic dynamical systems.

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The arithmetic Hodge index theorem for adelic line bundles

Abstract

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