What you actually compute

• Frobenius is not known exactly.
• Today we use a $p$-adic toric approach to compute Frobenius modulo $p^N$, for a chosen precision $N$.
• For a hypersurface, use a basis of differential forms on its affine complement.
• Apply Frobenius and reduce its images back to the basis to obtain the matrix modulo $p^N$.
• What matters here is the shape of the output: an approximation whose error you control.