Local heights of toric varieties over non-archimedean fields
Number Theory
2017-01-17 v2 Algebraic Geometry
Abstract
We generalize results about local heights previously proved in the case of discrete absolute values to arbitrary non-archimedean absolute values of rank 1. First, this is done for the induction formula of Chambert-Loir and Thuillier. Then we prove the formula of Burgos--Philippon--Sombra for the toric local height of a proper normal toric variety in this more general setting. We apply the corresponding formula for Moriwaki's global heights over a finitely generated field to a fibration which is generically toric. We illustrate the last result in a natural example where non-discrete non-archimedean absolute values really matter.
Keywords
Cite
@article{arxiv.1512.06574,
title = {Local heights of toric varieties over non-archimedean fields},
author = {Walter Gubler and Julius Hertel},
journal= {arXiv preprint arXiv:1512.06574},
year = {2017}
}
Comments
67 pages. v2: Assumption in Theorem 2.5.8 corrected to support function; other minor changes