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arXiv · 1707.08043

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

Edisson Gallego·Danny A. J. Gomez-Ramirez·Juan D. Velez
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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.

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Edisson Gallego, Danny A. J. Gomez-Ramirez, Juan D. Velez. 2017-07-25. On Positive-Characteristic Semi-Parametric Local-Uniform Reductions of Varieties over Finitely Generated $\mathbb{Q}$-Algebras. https://doi.org/10.1007/s00025-017-0691-7

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