Peng-Ju Guan

Frobenius lifts and point counting for smooth curves

We describe an algorithm for computing the zeta function of a proper, smooth curve over a finite field $k$ of characteristic $p$, when the curve is given together with some auxiliary data, including a lift $C$ to the valuation ring in a finite extension of $\Q_p$. The algorithm is denominator-free if the ramification i...