Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field
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A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants.
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In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions. In complex algebraic geometry the objects of study are complex analytic varieties, on which we have a local notion of complex analysis, through which we may define meromorphic functions.
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