On the U-Invariant of P-Adic Function Fields

ABSTRACT

We show that a quadratic form defined over the rational function field ?(x ₁ , …, _{x n} ) of dimension at least 4.2 ⁿ  + 1 is isotropic over all fields ? _p (x ₁ , …, _{x n} ), except for finitely many primes. Partial results concerning the u-invariant of p-adic function fields are also shown.