Parametrization of geometric Beilinson--Bloch heights via adelic line bundles

2024/06/28 by Song, Yinchong · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.19912

Abstract

Let S be a quasi-projective smooth variety over complex field ℂ . For a smooth projective morphism π:X→ S , we will introduce a new height pairing CH^p_\hom(X/S) × CH^q_\hom(X/S) → \widetildePic(S) with \widetildePic(S) the group of geometric adelic line bundles in the sense of Yuan--Zhang. It essentially parametrizes the asymptotic height pairing introduced by Brosnan and Pearlstein. We will show that this asymptotic height pairing coincides with Beilinson--Bloch pairing under certain conditions.

Cited by

• Asymptotics of local height pairing
• Global pluripotential theory for adelic line bundles

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• Properties of the Beilinson Height Pairing
• Asymptotics of local height pairing
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