Splitting fields of conics and sums of squares of rational functions

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.


Published in:
Manuscripta Mathematica, 141, 3-4, 727-736
Year:
2013
Publisher:
New York, Springer Verlag
ISSN:
0025-2611
Laboratories:




 Record created 2013-10-01, last modified 2018-03-17


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