Classes in ${\mathrm{H}}_{p^m}^{n+1}(F)$ of lower exponent

Adam Chapman, Daniel Krashen, Kelly McKinnie

Let $F$ be a field of characteristic $p>0$. We prove that if a symbol $A=\omega \otimes {\beta }_1\otimes \cdots \otimes {\beta }_n$ in $H_{p^m}^{n+1}(F)$ is of exponent dividing $p^{m-1}$, then its s…