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

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-parametri...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Authors: Gallego, Edisson, Gomez-Ramirez, Danny A J, Velez, Juan D
Format: Article
Language:English
Subjects:
Integers
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1707.08043