English

Sums-of-Squares Formulas over Algebraically Closed Fields

Algebraic Geometry 2016-11-01 v2

Abstract

In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of sums-of-squares formulas over algebraically closed fields is independent of the characteristic. We make the bound on p explicit, and we prove that the existence of a sums-of-squares formula of fixed type over an algebraically closed field is theoretically (though not practically) computable.

Keywords

Cite

@article{arxiv.1510.05369,
  title  = {Sums-of-Squares Formulas over Algebraically Closed Fields},
  author = {Melissa Lynn},
  journal= {arXiv preprint arXiv:1510.05369},
  year   = {2016}
}
R2 v1 2026-06-22T11:23:21.952Z