Manuscripta Mathematica

, Volume 142, Issue 1–2, pp 257–271 | Cite as

Weak toroidalization over non-closed fields

  • Dan Abramovich
  • Jan DenefEmail author
  • Kalle Karu


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.

Mathematics Subject Classification

Primary 14E15 14B25 Secondary 14M25 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of LeuvenLeuven, HeverleeBelgium
  3. 3.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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