Karim Johannes Becher: On fields of $u$-invariant 4

becher@maths.ucd.ie

Submission: 2004, Sep 27

This note is motivated by the problem of determining the $u$-invariant of a field $F$ of characteristic different from two when it is known that $u(F(\sqrt{-1}))=4$. A criterion is given to decide whether $u(F)\leq 4$ in this situation.

2000 Mathematics Subject Classification: 11E04, 11E81

Keywords and Phrases: quadratic form, u-invariant, Pythagoras number, real field, power series field, function field of a curve

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