English

Weak toroidalization over non-closed fields

Algebraic Geometry 2013-03-28 v3

Abstract

We prove that any dominant morphism of algebraic varieties over a field k of characteristic zero can be transformed into a toroidal (hence monomial) morphism by projective birational modifications of source and target. This was previously proved by the first and third author when k is algebraically closed. Moreover we show that certain additional requirements can be satisfied.

Keywords

Cite

@article{arxiv.1010.6171,
  title  = {Weak toroidalization over non-closed fields},
  author = {Dan Abramovich and Jan Denef and Kalle Karu},
  journal= {arXiv preprint arXiv:1010.6171},
  year   = {2013}
}

Comments

15 pages. Several minor changes. To appear in Manuscripta Mathematica

R2 v1 2026-06-21T16:36:01.625Z