The behavior of the $u$-invariant of a field of characteristic 2 under finite extensions

Abstract

Let F be a field of characteristic 2. We define v(F) as the smallest integer n such that any n-fold quadratic Pfister form over F is isotropic. If L/F is any finite extension, we prove v{F) < v{L) < v(F)-\-l. The corresponding question for fields of characteristic ^ 2 is still open.