Abstract
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.
Citation
Juliette Bruce. Daniel Erman. "A probabilistic approach to systems of parameters and Noether normalization." Algebra Number Theory 13 (9) 2081 - 2102, 2019. https://doi.org/10.2140/ant.2019.13.2081
Information