Sums-of-squares formulas over algebraically closed fields

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 o...

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Bibliographic Details
Published in:Journal of algebra 2018-03, Vol.497, p.393-410
Main Author: Lynn, Melissa
Format: Article
Language:English
Subjects:
Algebraic geometry
Gröbner bases
Number theory
Sums-of-squares formulas
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.11.041