On the Berkovich double residue fields and birational models
Abstract
Just as a residue field can be considered for a point of an algebraic variety, we can also consider a residue field for a point of a Berkovich analytic space. This residue field is a valuation field in the algebraic sense. Then we can consider its residue field as a valuation field. We call it the Berkovich double residue field at the point. In this paper, we consider a point of the Berkovich analytification of an algebraic variety and identify the Berkovich double residue field at with the union of the residue fields at the center of in birational models. Besides, we concretely compute the Berkovich double residue field for any quasi monomial valuation.
Keywords
Cite
@article{arxiv.2007.03610,
title = {On the Berkovich double residue fields and birational models},
author = {Keita Goto},
journal= {arXiv preprint arXiv:2007.03610},
year = {2024}
}
Comments
38 pages. (v2) Expanded section 3 and 5. Some expositions were improved alongside other minor revisions. (v3) Minor correction to Theorem 1.2 and some improvements in the exposition. To appear in Tsukuba J. Math