Arithmetic intersection theory over adelic curves
Algebraic Geometry
2022-07-05 v1 Number Theory
Abstract
We establish an arithmetic intersection theory in the framework of Arakelov geometry over adelic curves. To each projective scheme over an adelic curve, we associate a multi-homogenous form on the group of adelic Cartier divisors, which can be written as an integral of local intersection numbers along the adelic curve. The integrability of the local intersection number is justified by using the theory of resultants.
Cite
@article{arxiv.2103.15646,
title = {Arithmetic intersection theory over adelic curves},
author = {Huayi Chen and Atsushi Moriwaki},
journal= {arXiv preprint arXiv:2103.15646},
year = {2022}
}