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 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-Lorenzini and Chinburg-Moret-Bailly-Pappas-Taylor on Noether normalizations of projective families over the integers.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2016
- DOI:
- arXiv:
- arXiv:1604.01704
- Bibcode:
- 2016arXiv160401704B
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 13B02;
- 14D10;
- 14G10;
- 14G15;
- 11G25
- E-Print:
- 20 pages. Minor revisions to exposition