On $p$-schemes of order $p^3$

Jung Rae Cho, Mitsugu Hirasaka, Kijung Kim

Let $(X,S)$ be a $p$-scheme of order $p^3$ and $T$ the thin residue of $S$. Now we assume that $T$ has valency $p^2$. It is easy to see that one of the following holds: (i) $|T|=p^…