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Results in Mathematics

, Volume 72, Issue 1–2, pp 937–945 | Cite as

On Positive-Characteristic Semi-parametric Local Uniform Reductions of Varieties over Finitely Generated \(\mathbb {Q}\)-Algebras

  • Edisson Gallego
  • Danny Arlen de Jesús Gómez-RamírezEmail author
  • Juan D. Vélez
Open Access
Article

Abstract

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is equivalent to the existence of a collection of local semi-parametric (positive-characteristic) reductions of such variety for almost all primes (i.e. outside a finite set), and such that there exists a global complexity bounding all the corresponding structures involved. Results of this kind are a fundamental tool for transferring theorems in commutative algebra from a characteristic-zero setting to a positive-characteristic one.

Keywords

Lefschetz’s Principle height Radical ideal prime characteristic complexity 

Mathematics Subject Classification

03C20 03C98 13B99 11D72 11R99 

Notes

Acknowledgements

Open access funding provided by TU Wien (TUW). We would like to thank the reviewer and the editor for useful comments on the initial version of this manuscript. In addition, Danny Arlen de Jesús Gómez-Ramírez would like to thank C. Thompson for valuable suggestions during the writing process of this article. Finally, Danny Arlen de Jesús Gómez-Ramírez was supported by the Vienna Science and Technology Fund (WWTF) as part of the Vienna Research Group 12-004.

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Edisson Gallego
    • 1
  • Danny Arlen de Jesús Gómez-Ramírez
    • 2
    Email author
  • Juan D. Vélez
    • 3
  1. 1.University of AntioquiaMedellínColombia
  2. 2.Vienna University of TechnologyViennaAustria
  3. 3.National University of ColombiaMedellínColombia

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