A probabilistic approach to systems of parameters and Noether normalization
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 functionlike power series that enumerates higher dimensional varieties instead of closed points. This also yields a new proof of a recent result of GabberLiuLorenzini and ChinburgMoretBaillyPappasTaylor on Noether normalizations of projective families over the integers.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.01704
 Bibcode:
 2016arXiv160401704B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 13B02;
 14D10;
 14G10;
 14G15;
 11G25
 EPrint:
 20 pages. Minor revisions to exposition