The arithmetic Hodge index theorem for adelic line bundles

By Xinyi Yuan, Shou-wu Zhang. 2013

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f0c40917d27d45ea74009623db5a903a3e26415