Rationality of N\'eron-Tate height over function fields
Chengyuan Yang
TL;DR
This paper proves that the Néron-Tate height of subvarieties over function fields is always a rational number, using induction formulas and theta functions to characterize the canonical metric.
Contribution
It establishes the rationality of Néron-Tate heights over function fields, a result not previously known, by employing new techniques involving theta functions.
Findings
Néron-Tate heights are always rational over function fields
Characterization of the canonical metric via theta functions
Use of induction formula in the proof
Abstract
We prove that the N\'eron-Tate height of subvarieties are always rational numbers. We use the induction formula, and characterize the canonical metric by theta functions.
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Taxonomy
TopicsHistory and Theory of Mathematics · Algebraic Geometry and Number Theory