Tight closure/Monsky-quartic/Explicit non-inclusion/Fact

Let ${}{\mathbb {F} }_{q}={\mathbb {F} }_{p}(\alpha )$, ${}t\mapsto \alpha$, ${}\deg(\alpha )=d$. Set ${}Q=2^{d-1}$.

Then

${}xyf^{Q}\notin I^{[Q]}\,.$

Proof, Write another proof