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Title
On Positive-Characteristic Semi-parametric Local Uniform Reductions of Varieties over Finitely Generated Q-Algebras
AuthorGallego, Edisson ; Gómez-Ramírez, Danny Arlen de Jesús ; Vélez, Juan D.
Published in
Results in Mathematics, 2017, Vol. 72, Issue 1-2, page 937-945
PublishedSpringer Nature, 2017
LanguageEnglish
Document typeJournal Article
Keywords (EN)Lefschetzs Principle / height / Radical ideal / prime characteristic / complexity
ISSN1420-9012
URNurn:nbn:at:at-ubtuw:3-4258 Persistent Identifier (URN)
DOI10.1007/s00025-017-0691-7 
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 The work is publicly available
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On Positive-Characteristic Semi-parametric Local Uniform Reductions of Varieties over Finitely Generated Q-Algebras [0.43 mb]
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Abstract (English)

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.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License