, Volume 141, Issue 3-4, pp 727-736
Date: 06 Nov 2012

Splitting fields of conics and sums of squares of rational functions

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Abstract

Given a geometrically unirational variety over an infinite base field, we show that every finite separable extension of the base field that splits the variety is the residue field of a closed point. As an application, we obtain a characterization of function fields of smooth conics in which every sum of squares is a sum of two squares.