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.
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Grimm, D. Splitting fields of conics and sums of squares of rational functions. manuscripta math. 141, 727–736 (2013). https://doi.org/10.1007/s00229-012-0590-x
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DOI: https://doi.org/10.1007/s00229-012-0590-x