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arXiv · 2409.00611

Abstract divisorial spaces and arithmetic intersection numbers

Yulin Cai·Walter Gubler
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Abstract

Yuan and Zhang introduced arithmetic intersection numbers for adelic line bundles on quasi-projective varieties over a number field. Burgos and Kramer generalized this approach allowing more singular metrics at archimedean places. We introduce abstract divisorial spaces as a tool to generalize these arithmetic intersection numbers to the setting of a proper adelic base curve in the sense of Chen and Moriwaki. We also allow more singular metrics at non-archimedean places using relative mixed energy there as well.

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Yulin Cai, Walter Gubler. 2024-09-01. Abstract divisorial spaces and arithmetic intersection numbers. https://arxiv.org/abs/2409.00611

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