The First Monsky-Washnitzer Cohomology Group

The Monsky-Washnitzer cohomology and the de Rham cohomology

The author constructs a theory of dagger formal schemes over R and then defines the de Rham cohomology for flat dagger formal schemes X with integral and regular reductions X̄ which generalizes the MonskyWashnitzer cohomology. Finally the author gets Lefschetz’ fixed pointed formula for X with certain conditions.

Counting points on Cab curves using Monsky-Washnitzer cohomology

We describe an algorithm to compute the zeta function of any Cab curve over any finite field Fpn . The algorithm computes a p-adic approximation of the characteristic polynomial of Frobenius by computing in the Monsky-Washnitzer cohomology of the curve and thus generalizes Kedlaya’s algorithm for hyperelliptic curves. For fixed p the asymptotic running time for a Cab curve of genus g over Fpn i...

Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field Fpn of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over Fpn with a rational Weierstrass point is O(g4+ǫn3+ǫ).

Integral Monsky-washnitzer Cohomology and the Overconvergent De Rham-witt Complex

In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we pro...

An Algorithm for Computing p-Adic Heights Using Monsky-Washnitzer Cohomology