Quartic surface
$X = Z(y^4 - x^3 z + y z^3 + z w^3 + w^4) \subset \mathbf{P}^3_{\mathbf{C}}$
$p=31,\quad N=5$
| factor of $p^{-1}\operatorname{Frob}_p$ | dimension | liftable dimension, at most |
|---|
| $t-1$ | $1$ | $1$ |
| $t-1$ | $1$ | $1$ |
| $(t+1)^2$ | $2$ | $2$ |
- $\rho(X_{\mathbf{F}_{31}^{\mathrm{al}}}) = 4$
- no cycle obstruction found while working $\mathbf{Z}/(p)^5$
by searching for lines Elsenhans-Jahnel's method would have succeeded in this example
at $p = 31$ the reduction bound is already the sharp value 4, so there is nothing left to remove;