A bound on the index of exponent-$4$ algebras in terms of the $u$-invariant

Karim Johannes Becher, Fatma Kader Bingöl

For a prime number $p$, an integer $e\ge 2$ and a field $F$ containing a primitive $p^e$-th root of unity, the index of central simple $F$-algebras of exponent $p^e$ is bounded in…