The Monsky-Washnitzer cohomology and the de Rham cohomology
نویسنده
چکیده
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.
منابع مشابه
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...
متن کاملOverconvergent De Rham-witt Cohomology
The goal of this work is to construct, for a smooth variety X over a perfect field k of finite characteristic, an overconvergent de Rham-Witt complex W ΩX/k as a suitable subcomplex of the de RhamWitt complex of Deligne-Illusie. This complex, which is functorial in X, is a complex of étale sheaves and a differential graded algebra over the ring W (OX) of overconvergent Witt-vectors. If X is aff...
متن کاملCounting 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).
متن کاملFiniteness of De Rham Cohomology in Rigid Analysis
For a large class of smooth dagger spaces—rigid spaces with overconvergent structure sheaf—we prove finite dimensionality of de Rham cohomology. This is enough to obtain finiteness of P. Berthelot’s rigid cohomology also in the nonsmooth case. We need a careful study of de Rham cohomology in situations of semistable reduction. Introduction Let R be a complete discrete valuation ring of mixed ch...
متن کاملCounting 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...
متن کامل