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A
probabilistic approach to systems of parameters and Noether
normalization
Juliette Bruce and Daniel Erman |
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Vol. 13 (2019), No. 9, 2081–2102
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Abstract |
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We study systems of parameters over finite fields from a probabilistic perspective and use this to give the first effective Noether normalization result over a finite field. Our central technique is an adaptation of Poonen’s closed point sieve, where we sieve over higher dimensional subvarieties, and we express the desired probabilities via a zeta function-like power series that enumerates higher dimensional varieties instead of closed points. This also yields a new proof of a recent result of Gabber, Liu and Lorenzini (2015) and Chinburg, Moret-Bailly, Pappas and Taylor (2017) on Noether normalizations of projective families over the integers. |
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Keywords
Noether normalization, system of parameters, closed point
sieve
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Mathematical Subject Classification 2010
Primary: 13B02
Secondary: 11G25, 14D10, 14G10, 14G15
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Milestones
Received: 23 May 2018
Revised: 18 December 2018
Accepted: 27 June 2019
Published: 7 December 2019
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Authors |
| Juliette Bruce | |
| Department of Mathematics University of Wisconsin Madison, WI United States |
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| Daniel Erman | |
| Department of Mathematics University of Wisconsin Madison, WI United States |
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