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Publication# Splitting fields of conics and sums of squares of rational functions

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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Rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The co

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