Abstract divisorial spaces and arithmetic intersection numbers
Algebraic Geometry
2026-05-18 v2 Number Theory
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.
Cite
@article{arxiv.2409.00611,
title = {Abstract divisorial spaces and arithmetic intersection numbers},
author = {Yulin Cai and Walter Gubler},
journal= {arXiv preprint arXiv:2409.00611},
year = {2026}
}
Comments
97 pages, revision based on a referee report