Gallego, E., Gómez-Ramírez, D. A. de J., & Vélez, J. D. (2017). On Positive-Characteristic Semi-parametric Local Uniform Reductions of Varieties over Finitely Generated Q-Algebras. Results in Mathematics. https://doi.org/10.1007/s00025-017-0691-7
E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
Results in Mathematics
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ISSN:
1422-6383
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Date (published):
Sep-2017
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Publisher:
Birkhäuser
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Peer reviewed:
Yes
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Keywords:
Lefschetz’s Principle; height; Radical ideal; prime characteristic; complexity
en
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.